bluuebunny/crossref_metadata_2025 huggingface dataset:
Identification and Characterization of Preventable Adverse Drug Events in Family Medicine Clinics from Central Saudi Arabia
Authors: Assiri Ghadah A. , Bin Shihah Abdulelah S. , Alkhalifah Mohammed K. , Alshehri Ali S. , Alkhenizan Abdullah H.
Published: January 2023

Background:

Medication errors can result in adverse drug events (ADEs) and cause considerable patient harm. Limited data are available from Saudi Arabia and the Middle East regarding the prevalence of preventable adverse drug events (pADEs) in primary care settings.

Objectives:

To estimate the period prevalence of pADEs and assess the medication error severity in primary care setting in Saudi Arabia.

Methods:

This retrospective study is a continuation of a previous study where 117 of 2000 adult patients managed at the Family Medicine clinics of King Faisal Specialist Hospital and Research Center, Riyadh, Saudi Arabia, were identified to have had least one medication error in the past 15 months. The electronic health records of these 117 patients were analyzed for a 3-month post-medication error period to explore the presence of pADE. Medication errors were categorized according to the National Coordinating Council for Medication Error Reporting and Prevention index (NCC MERP) and the occurrence of pADE was assessed using the NCC MERP scheme.

Results:

Of the included 117 patients, 9 (7.7% [95% confidence interval (CI): 2.79–12.59]) experienced pADE (Category E), while 108 (92.3% [95% CI: 87.97–98.35]) did not (Category C). All patients who experienced pADE were using over-the-counter medications and were on polypharmacy. Outcomes 2a and 2b (asthma and β-blocker) accounted for two and four cases, respectively, while Outcomes 6 (warfarin and international normalized ratio), 7 (lithium and lithium level), 16 (new oral anti-coagulant or warfarin and antiplatelet), and 17 (acetylsalicylic acid [aspirin] and antiplatelet) each accounted for one case.

Conclusions:

This study provides the period prevalence of patients with pADEs from Family Medicine clinics at a major tertiary hospital of Saudi Arabia, and highlights the need for a multicenter study of clinically important medication errors at the prescribing and monitoring stages for the development of quality improvement programs.
Metallic implant-associated lymphoma: ALK-negative anaplastic large cell lymphoma associated with total knee replacement arthroplasty
Authors: Go Jai-Hyang
Published: January 2023

Metallic implant-associated lymphomas are extremely rare. Only seven cases have been reported in association with knee joint arthroplasty, and all tumors were large B-cell lymphomas. This report is the first case of anaplastic large cell lymphoma occurring after total knee replacement arthroplasty. An 80‑year‑old female patient was admitted because of right knee pain for 2 years. She had undergone total knee replacement arthroplasty 10 years prior. Computed tomography showed an irregular osteolytic lesion in the right lateral femoral condyle, adjacent to the metallic prosthesis. Histologic findings reveal sheets of anaplastic tumor cells that were positive for CD2, CD4, CD5, CD43, and CD30 but negative for CD3, CD20, CD15, and anaplastic lymphoma kinase. Epstein-Barr encoding region in situ hybridization was negative. Analysis of T-cell receptor γ gene rearrangement studies using BIOMED-2–based multiplex polymerase chain reaction confirmed monoclonal T cell proliferation. The woman was finally diagnosed with ALK-negative anaplastic large cell lymphoma.
Étale cohomology of rigid analytic spaces
Authors: de Jong Johan , van der Put Marius
Published: January 2023

The paper serves as an introduction to étale cohomology of rigid analytic spaces. A number of basic results are proved, e.g. concerning cohomological dimension, base change, invariance for change of base fields, the homotopy axiom and comparison for étale cohomology of algebraic varieties. The methods are those of classical rigid analytic geometry and along the way a number of known results on rigid cohomology are re-established.
Tamagawa numbers for motives with (non-commutative) coefficients
Authors: Burns D. , Flach M.
Published: January 2023

Let

M

be a motive which is defined over a number field and admits an action of a finite dimensional semisimple

\mathbb Q

-algebra

A

. We formulate and study a conjecture for the leading coefficient of the Taylor expansion at 0 of the

A

-equivariant

L

-function of

M

. This conjecture simultaneously generalizes and refines the Tamagawa number conjecture of Bloch, Kato, Fontaine, Perrin-Riou et al. and also the central conjectures of classical Galois module theory as developed by Fröhlich, Chinburg, M. Taylor et al. The precise formulation of our conjecture depends upon the choice of an order

\mathfrak A

in

A

for which there exists a 'projective

\mathfrak A

-structure' on

M

. The existence of such a structure is guaranteed if

\mathfrak A

is a maximal order, and also occurs in many natural examples where

\mathfrak A

is non-maximal. In each such case the conjecture with respect to a non-maximal order refines the conjecture with respect to a maximal order. We develop a theory of determinant functors for all orders in

A

by making use of the category of virtual objects introduced by Deligne.
$C^*$-algebras associated with presentations of subshifts
Authors: Matsumoto Kengo
Published: January 2023

A

\lambda

-graph system is a labeled Bratteli diagram with an upward shift except the top vertices. We construct a continuous graph in the sense of V. Deaconu from a

\lambda

-graph system. It yields a Renault's groupoid

C^*

-algebra by following Deaconu's construction. The class of these

C^*

-algebras generalize the class of

C^*

-algebras associated with subshifts and hence the class of Cuntz-Krieger algebras. They are unital, nuclear, unique

C^*

-algebras subject to operator relations encoded in the structure of the

\lambda

-graph systems among generating partial isometries and projections. If the

\lambda

-graph systems are irreducible (resp. aperiodic), they are simple (resp. simple and purely infinite). K-theory formulae of these

C^*

-algebras are presented so that we know an example of a simple and purely infinite

C^*

-algebra in the class of these

C^*

-algebras that is not stably isomorphic to any Cuntz-Krieger algebra.
Maximal indexes of Tits algebras
Authors: Merkurjev A.S.
Published: January 2023

Let

G

be a split simply connected semisimple algebraic group over a field

F

and let

C

be the center of

G

. It is proved that the maximal index of the Tits algebras of all inner forms of

G_L

over all field extensions

L/F

corresponding to a given character

\chi

of

C

equals the greatest common divisor of the dimensions of all representations of

G

which are given by the multiplication by

\chi

being restricted to

C

. An application to the discriminant algebra of an algebra with an involution of the second kind is given.
On the uniqueness problem of bivariant Chern classes
Authors: Yokura Shoji
Published: January 2023

In this paper we show that the bivariant Chern class

\gamma: {\Bbb F} \to {\Bbb H}

for morphisms from possibly singular varieties to nonsingular varieties are uniquely determined, which therefore implies that the Brasselet bivariant Chern class is unique for cellular morphisms with nonsingular target varieties. Similarly we can see that the Grothendieck transformation

\tau : {\Bbb K}_{alg} \to {\Bbb H}_{\Bbb Q}

constructed by Fulton and MacPherson is also unique for morphisms with nonsingular target varieties.
Homology stability for unitary groups
Authors: Mirzaii B. , van der Kallen W.
Published: January 2023

In this paper the homology stability for unitary groups over a ring with finite unitary stable rank is established. First we develop a 'nerve theorem' on the homotopy type of a poset in terms of a cover by subposets, where the cover is itself indexed by a poset. We use the nerve theorem to show that a poset of sequences of isotropic vectors is highly connected, as conjectured by Charney in the eighties. Homology stability of symplectic groups and orthogonal groups appear as a special case of our results.
Families of $p$-divisible groups with constant Newton polygon
Authors: Oort Frans , Zink Thomas
Published: January 2023

Let

X

be a

p

-divisible group with constant Newton polygon over a normal Noetherian scheme

S

. We prove that there exists an isogeny

X \to Y

such that

Y

admits a slope filtration. In case

S

is regular this was proved by N. Katz for dim

S = 1

and by T. Zink for dim

S \geq 1

.
The Gersten conjecture for Witt groups in the equicharacteristic case
Authors: Balmer Paul , Gille Stefan , Panin Ivan , Walter Charles
Published: January 2023

We prove the Gersten conjecture for Witt groups in the equicharacteristic case, that is for regular local rings containing a field of characteristic not 2.
The Farrell cohomology of $\mathrm{SP}(p-1, \mathbb{Z})$
Authors: Busch Cornelia
Published: January 2023

Let

p

be an odd prime with odd relative class number

h^-

. In this article we compute the Farrell cohomology of

\mathrm{Sp}(p-1,\mathbb Z)

, the first

p

-rank one case. This allows us to determine the

p

-period of the Farrell cohomology of

\mathrm{Sp}(p-1,\mathbb Z)

, which is

2y

, where

p-1=2^r y, y

odd. The

p

-primary part of the Farrell cohomology of

\mathrm{Sp}(p-1,\mathbb Z)

is given by the Farrell cohomology of the normalizers of the subgroups of order

p

in

\mathrm{Sp}(p-1,\mathbb Z)

. We use the fact that for odd primes

p

with

h^-

odd a relation exists between representations of

\mathbb Z/p\mathbb Z

in

\mathrm{Sp}(p-1,\mathbb Z)

and some representations of

\mathbb Z/p\mathbb Z

in

\mathrm{U}((p-1)/2)

.
On the classification of simple inductive limit $C^*$-algebras. I: The reduction theorem
Authors: Gong Guihua
Published: January 2023

Suppose that

A = \lim\limits_{n\to\infty}(A_n = \bigoplus_{i=1}^{t_n} M_{[n,i]}(C(X_{n,i})), \phi_{n,m})

is a simple

C^*

-algebra, where

X_{n,i}

are compact metrizable spaces of uniformly bounded dimensions (this restriction can be relaxed to a condition of very slow dimension growth). It is proved in this article that

A

can be written as an inductive limit of direct sums of matrix algebras over certain special 3-dimensional spaces. As a consequence it is shown that this class of inductive limit

C^*

-algebras is classified by the Elliott invariant – consisting of the ordered K-group and the tracial state space – in a subsequent paper joint with G. Elliott and L. Li (Part II of this series). (Note that the

C^*

-algebras in this class do not enjoy the real rank zero property.)
Unimodular covers of multiples of polytopes
Authors: Bruns Winfried , Gubeladze Joseph
Published: January 2023

Let

P

be a

d

-dimensional lattice polytope. We show that there exists a natural number

c_d

, only depending on

d

, such that the multiples

cP

have a unimodular cover for every natural number

c\ge c_d

. Actually, an explicit upper bound for

c_d

is provided, together with an analogous result for unimodular covers of rational cones.
Boolean localization, in practice
Authors: Jardine J.F.
Published: January 2023

A new proof of the existence of the standard closed model structure for the category of simplicial presheaves on an arbitrary Grothendieck site is given. This proof uses the principle of Boolean localization.
The connection between May's axioms for a triangulated tensor product and Happel's description of the derived category of the quiver $D_4$
Authors: Keller Bernhard , Neeman Amnon
Published: January 2023

In an important recent paper citeMay01, May gave an axiomatic description of the properties of triangulated categories with a symmetric tensor product. The main point of the current article is that there are two other results in the literature which can be used to shed considerable light on May's work. The first is a construction of Verdier's, which appeared in Beilinson, Bernstein and Deligne's  cite[Prop. 1.1.11, pp. 24-25]BeiBerDel82. The second and more important is the beautiful work of Happel, in citeHappel87, which can be used to better organise May's axioms.
Group $C^*$-algebras as compact quantum metric spaces
Authors: Rieffel Marc A.
Published: January 2023

Let

\ell

be a length function on a group

G

, and let

M_{\ell}

denote the operator of pointwise multiplication by

\ell

on

\mathbf \ell^2(G)

. Following Connes,

M_{\ell}

can be used as a “Dirac” operator for

C_r^*(G)

. It defines a Lipschitz seminorm on

C_r^*(G)

, which defines a metric on the state space of

C_r^*(G)

. We investigate whether the topology from this metric coincides with the weak-* topology (our definition of a “compact quantum metric space”). We give an affirmative answer for

G = {\mathbb Z}^d

when

\ell

is a word-length, or the restriction to

{\mathbb Z}^d

of a norm on

{\mathbb R}^d

. This works for

C_r^*(G)

twisted by a 2-cocycle, and thus for non-commutative tori. Our approach involves Connes' cosphere algebra, and an interesting compactification of metric spaces which is closely related to geodesic rays.
On families of pure slope $L$-functions
Authors: Grosse-Klönne Elmar
Published: January 2023

Let

R

be the ring of integers in a finite extension

K

of

\mathbb{Q}_p

, let

k

be its residue field and let

\chi:\pi_1(X)\to R^{\times}=GL_{1}(R)

be a “geometric” rank one representation of the arithmetic fundamental group of a smooth affine

k

-scheme

X

. We show that the locally

K

-analytic characters

\kappa:R^{\times}\to\mathbb{C}_p^{\times}

are the

\mathbb{C}_p

-valued points of a

K

-rigid space

{\cal W}

and that

L(\kappa\circ\chi,T)=\prod_{\overline{x}\in X}\frac{1}{1-(\kappa \circ\chi)(Frob_{\overline{x}})T^{\deg(\overline{x})}},

viewed as a two variable function in

T

and

\kappa

, is meromorphic on

\mathbb{A}_{\mathbb{C}_p}^1\times{\cal W}

. On the way we prove, based on a construction of Wan, a slope decomposition for ordinary overconvergent (finite rank)

\sigma

-modules, in the Grothendieck group of nuclear

\sigma

-modules.
On the height of Calabi-Yau varieties in positive characteristic
Authors: van der Geer G. , Katsura T.
Published: January 2023

We study invariants of Calabi-Yau varieties in positive characteristic, especially the height of the Artin-Mazur formal group. We illustrate these results by Calabi-Yau varieties of Fermat and Kummer type.
Stability of Arakelov bundles and tensor products without global sections
Authors: Hoffmann Norbert
Published: January 2023

This paper deals with Arakelov vector bundles over an arithmetic curve, i.e. over the set of places of a number field. The main result is that for each semistable bundle E, there is a bundle F such that

E \otimes F

has at least a certain slope, but no global sections. It is motivated by an analogous theorem of Faltings for vector bundles over algebraic curves and contains the Minkowski-Hlawka theorem on sphere packings as a special case. The proof uses an adelic version of Siegel's mean value formula.
The reciprocity obstruction for rational points on compactifications of torsors under tori over fields with global duality
Authors: van Hamel Joost
Published: January 2023

This paper studies the reciprocity obstruction to the local–global principle for compactifications of torsors under tori over a generalised global field of characteristic zero. Under a non-divisibility condition on the second Tate–Shafarevich group for tori, it is shown that the reciprocity obstruction is the only obstruction to the local–global principle. This gives in particular an elegant unified proof of Sansuc's result on the Brauer–Manin obstruction for compactifications of torsors under tori over number fields, and Scheiderer's result on the reciprocity obstruction for compactifications of torsors under tori over

p

-adic function fields.
Diffeotopy functors of ind-algebras and local cyclic cohomology
Authors: Puschnigg Michael
Published: January 2023

We introduce a new bivariant cyclic theory for topological algebras, called local cyclic cohomology. It is obtained from bivariant periodic cyclic cohomology by an appropriate modification, which turns it into a deformation invariant bifunctor on the stable diffeotopy category of topological ind-algebras. We set up homological tools which allow the explicit calculation of local cyclic cohomology. The theory turns out to be well behaved for Banach- and

C^*

-algebras and possesses many similarities with Kasparov's bivariant operator K-theory. In particular, there exists a multiplicative bivariant Chern-Connes character from bivariant K-theory to bivariant local cyclic cohomology.
A motivic isomorphism between two projective homogeneous varieties under the action of a group of type $G_2$
Authors: Bonnet Jean-Paul
Published: January 2023

Dans tout cet article, on désigne par

k

un corps de caractéristique différente de 2 et on appelle variété tout

k

-schéma séparé et de type fini. L'objet du présent article est d'étudier

\mathcal X(\alpha_{1})

et

\mathcal X(\alpha_{2})

, les variétés homogènes projectives associées à chacune des deux racines d'un groupe de type

G_{2}

. La première d'entre elles,

\mathcal X(\alpha_{1})

, est une quadrique projective de dimension 5 associée à une voisine de Pfister et l'autre,

\mathcal X(\alpha_{2})

, est une variété de Fano (de genre

10

). Ces deux variétés ne sont pas isomorphes, pourtant elles le deviennent en tant qu'objets d'une catégorie plus large, à savoir la catégorie des correspondances (et par conséquent également dans la catégorie des motifs de Chow). Nous établissons que ce résultat est vrai que les variétés soient déployées ou non. En première partie, nous rappelons quelques résultats classiques sur les algèbres d'octonions et construisons un modèle d'algèbre d'octonions déployée. En seconde partie, étape importante de notre travail, nous construisons une structure cellulaire de

\mathcal X(\alpha_{2})

lorsqu'elle est déployée. C'est également dans cette partie que nous déterminons la structure de l'anneau de Chow déployé de la variété

\mathcal X(\alpha_{2})

. Enfin, en troisième partie, après avoir introduit nos notations et rappelé les résultats nécessaires sur la catégorie des correspondances, nous établissons l'isomorphisme motivique en toute généralité.
Essential dimension: A functorial point of view (after A. Merkurjev)
Authors: Berhuy Grégory , Favi Giordano
Published: January 2023

In these notes we develop a systematic study of the essential dimension of functors. This approach is due to A. Merkurjev and can be found in his unpublished notes [12]. The notion of essential dimension was earlier introduced for finite groups by J. Buhler and Z. Reichstein in [3] and for an arbitrary algebraic group over an algebraically closed field by Z. Reichstein in [14]. This is a numerical invariant depending on the group

G

and the field

k

. This number is denoted by

\operatorname{ed}_k(G)

. In this paper we insist on the behaviour of the essential dimension under field extension

k'/k

and try to compute

\operatorname{ed}_k(G)

for
any

k

. This will be done in particular for the group

\mathbb Z/n

when

n\leq5

and for the circle group. Along the way we define the essential dimension of functor with versal pairs and prove that all the different notions of essential dimension agree in the case of algebraic groups. Applications to finite groups are given. Finally we give a proof of the so-called homotopy invariance, that is

\operatorname{ed}_k(G)=\operatorname{ed}_{k(t)}(G)

, for an algebraic group

G

defined over an infinite field

k

.
$J_1(p)$ has connected fibers
Authors: Conrad Brian , Edixhoven Bas , Stein William
Published: January 2023

We study resolution of tame cyclic quotient singularities on arithmetic surfaces, and use it to prove that for any subgroup

H \subseteq (\Z/p\Z)^{\times}/\{\pm 1\}

the map

X_H(p) = X_1(p)/H \rightarrow X_0(p)

induces an injection

\Phi(J_H(p)) \rightarrow \Phi(J_0(p))

on mod

p

component groups, with image equal to that of

H

in

\Phi(J_0(p))

when the latter is viewed as a quotient of the cyclic group

(\Z/p\Z)^{\times}/\{\pm 1\}

. In particular,

\Phi(J_H(p))

is always Eisenstein in the sense of Mazur and Ribet, and

\Phi(J_1(p))

is trivial: that is,

J_1(p)

has connected fibers. We also compute tables of arithmetic invariants of optimal quotients of

J_1(p)

.
Enriched functors and stable homotopy theory
Authors: Dundas Bjørn Ian , Röndigs Oliver , Østvær Paul Arne
Published: January 2023

In this paper we employ enriched category theory to construct a convenient model for several stable homotopy categories. This is achieved in a three-step process by introducing the pointwise, homotopy functor and stable model category structures for enriched functors. The general setup is shown to describe equivariant stable homotopy theory, and we recover Lydakis' model category of simplicial functors as a special case. Other examples – including motivic homotopy theory – will be treated in subsequent papers.
Motivic functors
Authors: Dundas Bjørn Ian , Röndigs Oliver , Østvær Paul Arne
Published: January 2023

The notion of motivic functors refers to a motivic homotopy theoretic analog of continuous functors. In this paper we lay the foundations for a homotopical study of these functors. Of particular interest is a model structure suitable for studying motivic functors which preserve motivic weak equivalences and a model structure suitable for motivic stable homotopy theory. The latter model is Quillen equivalent to the category of motivic symmetric spectra. There is a symmetric monoidal smash product of motivic functors, and all model structures constructed are compatible with the smash product in the sense that we can do homotopical algebra on the various categories of modules and algebras. In particular, motivic cohomology is naturally described as a commutative ring in the category of motivic functors.
On the average values of the irreducible characters of finite groups of Lie type on geometric unipotent classes
Authors: Geck Meinolf
Published: January 2023

In 1980, Lusztig posed the problem of showing the existence of a unipotent support for the irreducible characters of a finite reductive group

G({\Bbb F}_q)

. This is defined in terms of certain average values of the irreducible characters on unipotent classes. The problem was solved by Lusztig [16] for the case where

q

is a power of a sufficiently large prime. In this paper we show that, in general, these average values can be expressed in terms of the Green functions of

G

. In good characteristic, these Green functions are given by polynomials in

q

. Combining this with Lusztig's results, we can then establish the existence of unipotent supports whenever

q

is a power of a good prime.
Separatedness in constructive topology
Authors: Bridges Douglas , Vîţă Luminiţa
Published: January 2023

We discuss three natural, classically equivalent, Hausdorff separation properties for topological spaces in constructive mathematics. Using Brouwerian examples, we show that our results are the best possible in our constructive framework.
Curvature properties of the Calabi-Yau moduli
Authors: Wang Chin-Lung
Published: January 2023

A curvature formula for the Weil-Petersson metric on the Calabi-Yau moduli spaces is given. Its relations to the Hodge metrics and the Bryant-Griffiths cubic form are obtained in the threefold case. Asymptotic behavior of the curvature near the boundary of moduli is also discussed via the theory of variations of Hodge structures.
Rigidity II: non-orientable case
Authors: Yagunov Serge
Published: January 2023

The following paper is devoted to the construction of transfer maps (Becker-Gottlieb transfers) for non-orientable cohomology theories on the category of smooth algebraic varieties. Since non-orientability makes obstruction to the existence of transfer structure, we define transfers for a specially constructed class of morphisms. Being rather small, this class is yet big enough for application purposes. As an application of the developed transfer technique we get the proof of rigidity theorem for all cohomology theories represented by T-spectra.
Comparison of abelian categories recollements
Authors: Franjou Vincent , Pirashvili Teimuraz
Published: January 2023

We give a necessary and sufficient condition for a morphism between recollements of abelian categories to be an equivalence.
On the scattering theory of the Laplacian with a periodic boundary condition. II. Additional channels of scattering
Authors: Frank Rupert L. , Shterenberg Roman G.
Published: January 2023

We study spectral and scattering properties of the Laplacian

H^{(\sigma)} = -\Delta

in

L_2(\mathbb R^2_+)

corresponding to the boundary condition

\frac{\partial u}{\partial \nu}+\sigma u=0

for a wide class of periodic functions

σ

. For non-negative

σ

we prove that

H^{(σ)}

is unitarily equivalent to the Neumann Laplacian

H^{(0)}

. In general, there appear additional channels of scattering which are analyzed in detail.
Adding tails to $C^*$-correspondences
Authors: Muhly Paul S. , Tomforde Mark
Published: January 2023

We describe a method of adding tails to

C^*

-correspondences which generalizes the process used in the study of graph

C^*

-algebras. We show how this technique can be used to extend results for augmented Cuntz-Pimsner algebras to

C^*

-algebras associated to general

C^*

-correspondences, and as an application we prove a gauge-invariant uniqueness theorem for these algebras. We also define a notion of relative graph

C^*

-algebras and show that properties of these

C^*

-algebras can provide insight and motivation for results about relative Cuntz-Pimsner algebras.
Chow groups with coefficients
Authors: Rost Markus
Published: January 2023

We develop a generalization of the classical Chow groups in order to have available some standard properties for homology theories: long exact sequences, spectral sequences for fibrations, homotopy invariance and intersections. The basis for our constructions is Milnor's

K

-theory.
Erratum to the paper “Absolute continuity of the spectrum of a Schrödinger operator with a potential which is periodic in some directions and decays in others”
Authors: Filonov N. , Klopp F.
Published: January 2023

Lemma 6.1 and 6.2 in [1] are false as stated there. Below, we correct the proof of Theorem 6.1 accordingly.
The free cover of a row contraction
Authors: Arveson William
Published: January 2023

We establish the existence and uniqueness of finite free resolutions - and their attendant Betti numbers - for graded commuting

d

-tuples of Hilbert space operators. Our approach is based on the notion of free cover of a (perhaps noncommutative) row contraction. Free covers provide a flexible replacement for minimal dilations that is better suited for higher-dimensional operator theory.
Asymptotic expansions for bounded solutions to semilinear Fuchsian equations
Authors: Liu Xiaochun , Witt Ingo
Published: January 2023

It is shown that bounded solutions to semilinear elliptic Fuchsian equations obey complete asymptotic expansions in terms of powers and logarithms in the distance to the boundary. For that purpose, Schulze's notion of asymptotic type for conormal asymptotic expansions near a conical point is refined. This in turn allows to perform explicit computations on asymptotic types – modulo the resolution of the spectral problem for determining the singular exponents in the asymptotic expansions.
Bounds for the anticanonical bundle of a homogeneous projective rational manifold
Authors: Snow Dennis
Published: January 2023

The following bounds for the anticanonical bundle

K_X^{*} = \det T_X

of a complex homogeneous projective rational manifold 

X

of dimension

n

are established: newcommandbinom[2]#1choose#2

3^n \le \dim H^0(X,K_X^{*}) \le \binom{2n+1}n\quad\mathrm{and}\quad 2^n n! \le \deg K_X^{*} \le (n+1)^n

with equality in the lower bounds if and only if

X

is a flag manifold and equality in the upper bounds if and only if

X

is complex projective space. None of these bounds holds for general Fano manifolds.
Applications of weight-two motivic cohomology
Authors: Kahn Bruno
Published: January 2023

Using Lichtenbaum's complex

\Gamma(2)

, we reprove and extend a little bit some known results relating the kernel of

H^3(F,{\bold Q}/{\bold Z}(2))\to H^3(F(X),{\bold Q}/{\bold Z}(2))

to the torsion of

CH^2 X

for rational varieties

X

.
On the values of equivariant zeta functions of curves over finite fields
Authors: Burns David
Published: January 2023

Let

K/k

be a finite Galois extension of global function fields of characteristic

p

. Let

C_K

denote the smooth projective curve that has function field

K

and set

G:= \operatorname{Gal}(K/k)

. We conjecture a formula for the leading term in the Taylor expansion at zero of the

G

-equivariant truncated Artin

L

-functions of

K/k

in terms of the Weil-étale cohomology of

\mathbb G_m

on the corresponding open subschemes of

C_K

. We then prove the

\ell

-primary component of this conjecture for all primes

\ell

for which either

\ell \not= p

or the relative algebraic

K

-group

K_0(\mathbb z _\ell [G],\mathbb Q_\ell)

is torsion-free. In the remainder of the manuscript we show that this result has the following consequences for

K/k

: if

p \nmid |G|

, then refined versions of all of Chinburg's '

\Omega

-Conjectures' in Galois module theory are valid; if the torsion subgroup of

K^\times

is a cohomologically-trivial

G

-module, then Gross's conjectural 'refined class number formula' is valid; if

K/k

satisfies a certain natural class-field theoretical condition, then Tate's recent refinement of Gross's conjecture is valid.
Some remarks on morphisms between Fano threefolds
Authors: Amerik Ekaterina
Published: January 2023

Let

X, Y

be Fano threefolds of Picard number one and such that the ample generators of Picard groups are very ample. Let

X

be of index one and

Y

be of index two. It is shown that the only morphisms from

X

to

Y

are double coverings. In fact nearly the whole paper is the analysis of the case where

Y

is the linear section of the Grassmannian

G(1,4)

, since the other cases were more or less solved in another article. This remaining case is treated with the help of Debarre's connectedness theorem for inverse images of Schubert cycles.
Calabi-Yau threefolds of quasi-product type
Authors: Oguiso Keiji
Published: January 2023

According to the numerical Iitaka dimension

\nu(X,D)

and

c_{2}(X) \cdot D

, fibered Calabi-Yau threefolds

\Phi_{|D|} : X \rightarrow W ({dim } W > 0)

are coarsely classified into six different classes. Among these six classes, there are two peculiar classes called of type

{II}_{0}

and of type

{III}_{0}

which are characterized respectively by

\nu(X,D) = 2

and

c_{2}(X) \cdot D = 0

and by

\nu(X,D) = 3

and

c_{2}(X) \cdot D = 0

. Fibered Calabi-Yau threefolds of type

{III}_{0}

are intensively studied by Shepherd-Barron, Wilson and the author and now there are a satisfactory structure theorem and the complete classification. The purpose of this paper is to guarantee a complete structure theorem of fibered Calabi-Yau threefolds of type

{II}_{0}

to finish the classification of these two peculiar classes. In the course of proof, the log minimal model program for threefolds established by Shokurov and Kawamata will play an important role. We shall also introduce a notion of quasi-product threefolds and show their structure theorem. This is a generalization of the notion of hyperelliptic surfaces to threefolds and will have other applicability, too.
Some sharp weighted estimates for multilinear operators
Authors: Liu Lanzhe
Published: January 2023

In this paper, we establish a sharp inequality for some multilinear operators related to certain integral operators. The operators include Calderón-Zygmund singular integral operator, Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator. As application, we obtain the weighted norm inequalities and

L\log L

type estimate for the multilinear operators.
Rational curves on homogeneous cones
Authors: Perrin Nicolas
Published: January 2023

A homogeneous cone

X

is the cone over a homogeneous variety

G/P

embedded thanks to an ample line bundle

L

. In this article, we describe the irreducible components of the scheme of morphisms of class

\alpha\in A_1(X)

from a rational curve to X. The situation depends on the line bundle L : if the projectivised tangent space to the vertex contains lines then the irreducible components are described by the difference between Cartier and Weil divisors. On the contrary if there is no line in the projectivised tangent space to the vertex then there are new irreducible components corresponding to the multiplicity of the curve through the vertex.
Matsumoto $K$-groups associated to certain shift spaces
Authors: Carlsen Toke Meier , Eilers Søren
Published: January 2023

In [24] Matsumoto associated to each shift space (also called a subshift) an Abelian group which is now known as Matsumoto's

K_0

-group. It is defined as the cokernel of a certain map and resembles the first cohomology group of the dynamical system which has been studied in for example [2], [28], [13], [16] and [11] (where it is called the dimension group).

In this paper, we will for shift spaces having a certain property

(*)

, show that the first cohomology group is a factor group of Matsumoto's

K_0

-group. We will also for shift spaces having an additional property

(**)

, describe Matsumoto's

K_0

-group in terms of the first cohomology group and some extra information determined by the left special elements of the shift space.

We determine for a broad range of different classes of shift spaces if they have property

(*)

and property

(**)

and use this to show that Matsumoto's

K_0

-group and the first cohomology group are isomorphic for example for finite shift spaces and for Sturmian shift spaces.

Furthermore, the ground is laid for a description of the Matsumoto

K_0

-group as an emphordered group in a forthcoming paper.
Arakelov invariants of Riemann surfaces
Authors: de Jong Robin
Published: January 2023

We derive closed formulas for the Arakelov-Green function and the Faltings delta-invariant of a compact Riemann surface.
The projected single-particle Dirac operator for Coulombic potentials
Authors: Jakubassa-Amundsen D.H.
Published: January 2023

A sequence of unitary transformations is applied to the one-electron Dirac operator in an external Coulomb potential such that the resulting operator is of the form

\Lambda_+ A\,\Lambda_+\,+\Lambda_-A\,\Lambda_-\;

to any given order in the potential strength, where

\Lambda_+

and

\Lambda_-

project onto the positive and negative spectral subspaces of the free Dirac operator. To first order,

\Lambda_+ A \,\Lambda_+

coincides with the Brown-Ravenhall operator. Moreover, there exists a simple relation to the Dirac operator transformed with the help of the Foldy-Wouthuysen technique. By defining the transformation operators as integral operators in Fourier space it is shown that they are well-defined and that the resulting transformed operator is

p

-form bounded. In the case of a modified Coulomb potential,

V=-\gamma x^{-1+\epsilon},\;\;\epsilon >0,\;

one can even prove subordinacy of the

n

-th order term in

\gamma

with respect to the

n-1

st order term for all

n>1

, as well as their

p

-form boundedness with form bound less than one.
Algebraic $K$-theory and sums-of-squares formulas
Authors: Dugger Daniel , Isaksen Daniel C.
Published: January 2023

We prove a result about the existence of certain 'sums-of-squares' formulas over a field

F

. A classical theorem uses topological

K

-theory to show that if such a formula exists over

\mathbb R

, then certain powers of 2 must divide certain binomial coefficients. In this paper we use algebraic

K

-theory to extend the result to all fields not of characteristic 2.
Some remarks on morphisms between Fano threefolds: Erratum [cf. Doc. Math. J. DMV 9, 471–486 (2004; Zbl 1072.14048)]
Authors: Amerik Ekaterina
Published: January 2023

It was pointed out to me by James McKernan that there is a mistake in the proof of Proposition 2.7. Namely, it is stated (and “used”) there that the complement to a smooth conic in

\mathbb{P}^2

is simply-connected. This is obviously false; indeed, the fundamental group is cyclic of order two. This mistake is, however, easy to deal with.
The distribution of group structures on elliptic curves over finite prime fields
Authors: Gekeler Ernst-Ulrich
Published: January 2023

We determine the probability that a randomly chosen elliptic curve

E/{\mathbb F}_p

over a randomly chosen prime field

{\mathbb F}_p

has an

{\ell}

-primary part

E({\mathbb F}_p) [\ell^{\infty}]

isomorphic with a fixed abelian

\ell

-group

H^{(\ell)}_{\alpha,\beta} = {\mathbb Z}/{\ell}^{\alpha} \times {\mathbb Z}/\ell^{\beta}

.

Probabilities for “

|E(\mathbb F_p)|

divisible by

n

”, “

E(\mathbb F_p)

cyclic and expectations for the number of elements of precise order

n

in

E(\mathbb F_p)

are derived, both for unbiased

E/\mathbb F_p

and for

E/\mathbb F_p

with

p \equiv 1 (\ell^r)

.
Galois coverings, Morita equivalence and smash extensions of categories over a field.
Authors: Cibils Claude , Solotar Andrea
Published: January 2023

Algebras over a field

k

generalize to categories over

k

in order to considers Galois coverings. Two theories presenting analogies, namely smash extensions and Galois coverings with respect to a finite group are known to be different. However we prove in this paper that they are Morita equivalent. For this purpose we need to describe explicit processes providing Morita equivalences of categories which we call contraction and expansion. A structure theorem is obtained: composition of these processes provides any Morita equivalence up to equivalence, a result which is related with the karoubianisation (or idempotent completion) and additivisation of a

k

-category.
On packing spheres into containers
Authors: Schürmann Achill
Published: January 2023

In an Euclidean

d

-space, the container problem asks to pack

n

equally sized spheres into a minimal dilate of a fixed container. If the container is a smooth convex body and

d\geq 2

we show that solutions to the container problem can not have a “simple structure” for large

n

. By this we in particular find that there exist arbitrary small

r>0

, such that packings in a smooth,

3

-dimensional convex body, with a maximum number of spheres of radius

r

, are necessarily not hexagonal close packings. This contradicts Kepler's famous statement that the cubic or hexagonal close packing “will be the tightest possible, so that in no other arrangement more spheres could be packed into the same container”.
Second order freeness and fluctuations of random matrices. III: Higher order freeness and free cumulants
Authors: Collins Benoît , Mingo James A. , Śniady Piotr , Speicher Roland
Published: January 2023

We extend the relation between random matrices and free probability theory from the level of expectations to the level of all correlation functions (which are classical cumulants of traces of products of the matrices). We introduce the notion of “higher order freeness” and develop a theory of corresponding free cumulants. We show that two independent random matrix ensembles are free of arbitrary order if one of them is unitarily invariant. We prove

\mathrm{R}

-transform formulas for second order freeness. Much of the presented theory relies on a detailed study of the properties of “partitioned permutations”.
The Hirzebruch-Mumford volume for the orthogonal group and applications
Authors: Gritsenko V. , Hulek K. , Sankaran G.K.
Published: January 2023

In this paper we derive an explicit formula for the Hirzebruch-Mumford volume of an indefinite lattice

L

of rank

\ge 3

. If

\Gamma \subset \mathrm O(L)

is an arithmetic subgroup and

L

has signature

(2,n)

, then an application of Hirzebruch-Mumford proportionality allows us to determine the leading term of the growth of the dimension of the spaces

S_k(\Gamma)

of cusp forms of weight

k

, as

k

goes to infinity. We compute this in a number of examples, which are important for geometric applications.
Equivariant local cyclic homology and the equivariant Chern-Connes character
Authors: Voigt Christian
Published: January 2023

We define and study equivariant analytic and local cyclic homology for smooth actions of totally disconnected groups on bornological algebras. Our approach contains equivariant entire cyclic cohomology in the sense of Klimek, Kondracki and Lesniewski as a special case and provides an equivariant extension of the local cyclic theory developped by Puschnigg. As a main result we construct a multiplicative Chern-Connes character for equivariant

KK

-theory with values in equivariant local cyclic homology.
Selmer groups and torsion zero cycles on the selfproduct of a semistable elliptic curve
Authors: Langer Andreas
Published: January 2023

In this paper we extend the finiteness result on the

p

-primary torsion subgroup in the Chow group of zero cycles on the selfproduct of a semistable elliptic curve obtained in joint work with S. Saito to primes

p

dividing the conductor. On the way we show the finiteness of the Selmer group associated to the symmetric square of the elliptic curve for those primes. The proof uses

p

-adic techniques, in particular the Fontaine-Jannsen conjecture proven by Kato and Tsuji.
Isotropy of quadratic spaces in finite and infinite dimension
Authors: Becher Karim Johannes , Hoffmann Detlev W.
Published: January 2023

In the late 1970s, Herbert Gross asked whether there exist fields admitting anisotropic quadratic spaces of arbitrarily large finite dimensions but none of infinite dimension. We construct examples of such fields and also discuss related problems in the theory of central simple algebras and in Milnor

K

-theory.
Generic observability of dynamical systems
Authors: Yazdani Esfandiar Nava
Published: January 2023

We deal with a certain observation mapping defined by means of weighted measurments on a dynamical system and give necessary and sufficient conditions, under which this mapping is generically an injective immersion.
Rational real algebraic models of topological surfaces
Authors: Biswas Indranil , Huisman Johannes
Published: January 2023

Comessatti proved that the set of all real points of a rational real algebraic surface is either a nonorientable surface, or diffeomorphic to the sphere or the torus. Conversely, it is well known that each of these surfaces admits at least one rational real algebraic model. We prove that they admit exactly one rational real algebraic model. This was known earlier only for the sphere, the torus, the real projective plane and the Klein bottle.
Visibility of Mordell-Weil groups
Authors: Stein William A.
Published: January 2023

We introduce a notion of visibility for Mordell-Weil groups, make a conjecture about visibility, and support it with theoretical evidence and data. These results shed new light on relations between Mordell-Weil and Shafarevich-Tate groups.
Visibility of the Shafarevich-Tate group at higher level
Authors: Jetchev Dimitar P. , Stein William A.
Published: January 2023

We study visibility of Shafarevich–Tate groups of modular abelian varieties in Jacobians of modular curves of higher level. We prove a theorem about the existence of visible elements at a specific higher level under certain hypothesis which can be verified explicitly. We also provide a table of examples of visible subgroups at higher level and state a conjecture inspired by our data.
Hirzebruch-Mumford proportionality and locally symmetric varieties of orthogonal type
Authors: Gritsenko V. , Hulek K. , Sankaran G.K.
Published: January 2023

For many classical moduli spaces of orthogonal type there are results about the Kodaira dimension. But nothing is known in the case of dimension greater than

19

. In this paper we obtain the first results in this direction. In particular the modular variety defined by the orthogonal group of the even unimodular lattice of signature

(2,8m+2)

is of general type if

m\ge 5

.
The Euler characteristic of a category
Authors: Leinster Tom
Published: January 2023

The Euler characteristic of a finite category is defined and shown to be compatible with Euler characteristics of other types of object, including orbifolds. A formula is proved for the cardinality of a colimit of sets, generalizing the classical inclusion-exclusion formula. Both rest on a generalization of Rota's Möbius inversion from posets to categories.
On tameness and growth conditions
Authors: Winkelmann Jörg
Published: January 2023

We study discrete subsets of

C^d

, relating «tameness» with growth conditions.
Dynamical symmetries in supersymmetric matrix models
Authors: Bach V. , Hoppe J. , Lundholm D.
Published: January 2023

We reveal a dynamical

\operatorname{SU}(2)

symmetry in the asymptotic description of supersymmetric matrix models. We also consider a recursive approach for determining the ground state, and point out some additional properties of the model(s).
Secondary invariants for Frechet algebras and quasihomomorphisms
Authors: Perrot Denis
Published: January 2023

A Fréchet algebra endowed with a multiplicatively convex topology has two types of invariants: homotopy invariants (topological

K

-theory and periodic cyclic homology) and secondary invariants (multiplicative

K

-theory and the non-periodic versions of cyclic homology). The aim of this paper is to establish a Riemann-Roch-Grothendieck theorem relating direct images for homotopy and secondary invariants of Fréchet

m

-algebras under finitely summable quasihomomorphisms.
Semigroup crossed products and Hecke algebras arising from number fields
Authors: Arledge Jane , Laca Marcelo , Raeburn Iain
Published: January 2023

Recently Bost and Connes considered a Hecke

C^*

-algebra arising from the ring inclusion of

\Bbb Z

in

\Bbb Q

, and a

C^*

-dynamical system involving this algebra. Laca and Raeburn realized this algebra as a semigroup crossed product, and studied it using techniques they had previously developed for studying Toeplitz algebras. Here we associate Hecke algebras to general number fields, realize them as semigroup crossed products, and analyze their representations.
On the 2-typical de Rham-Witt complex
Authors: Costeanu Viorel
Published: January 2023

In this paper we introduce the 2-typical de Rham-Witt complex for arbitrary commutative, unital rings and log-rings. We describe this complex for the rings

\Z

and

\Z_{(2)}

, for the log-ring

(\Z_{(2)},M)

with the canonical log-structure, and we describe its behaviour under polynomial extensions. In an appendix we also describe the

p

-typical de Rham-Witt complex of

(\Z_{(p)},M)

for

p

odd.
$K$-theory of log-schemes. I.
Authors: Nizioł Wiesława
Published: January 2023

We set down some basic facts about the algebraic and topological

K

-theory of log-schemes. In particular, we show that the l-adic topological log-étale

K

-theory of log-regular schemes computes the l-adic étale

K

-theory of the largest open sets where the log-structure is trivial.
Arithmetic of Hermitian forms
Authors: Shimura Goro
Published: January 2023

We investigate the following two problems on a hermitian form

\Phi

over an algebraic number field: (1) classification of

\Phi

over the ring of algebraic integers; (2) hermitian Diophantine equations. The same types of problems for quadratic forms were treated in the author's previous articles. Here we discuss the hermitian case. Problem (2) concerns an equation

\xi\Phi\cdot {}^t\xi^{\rho}=\Psi

, where

\Phi

and

\Psi

represent hermitian forms. We connect the number of such

\xi

modulo a group of units with the class number and mass of the unitary group of a form

\Theta

such that

\Phi\approx\Psi\oplus\Theta

.
The critical values of certain Dirichlet series
Authors: Shimura Goro
Published: January 2023

We investigate the values of several types of Dirichlet series

D(s)

for certain integer values of

s,

and give explicit formulas for the value

D(s)

in many cases. The easiest types of

D

are Dirichlet

L

-functions and their variations; a somewhat more complex case involves elliptic functions. There is one new type that includes

\sum_{n=1}^{\infty} (n^2+1)^{-s}

for which such values have not been studied previously.