bluuebunny/crossref_metadata_2025 huggingface dataset:
A Framework for Exactrac Dynamic Commissioning for Stereotactic Radiosurgery and Stereotactic Ablative Radiotherapy
Authors: Perrett Ben , Ukath Jaysree , Horgan Emma , Noble Chris , Ramachandran Prabhakar
Published: January 2023

This paper aims to provide guidance and a framework for commissioning tests and tolerances for the ExacTrac Dynamic image-guided and surface-guided radiotherapy (SGRT) system. ExacTrac Dynamic includes a stereoscopic X-ray system, a structured light projector, stereoscopic cameras, thermal camera for SGRT, and has the capability to track breath holds and internal markers. The system provides fast and accurate image guidance and intrafraction guidance for stereotactic radiosurgery and stereotactic ablative radiotherapy. ExacTrac Dynamic was commissioned on a recently installed Elekta Versa HD. Commissioning tests are described including safety, isocenter calibration, dosimetry, image quality, data transfer, SGRT stability, SGRT localization, gating, fusion, implanted markers, breath hold, and end-to-end testing. Custom phantom designs have been implemented for assessment of the deep inspiration breath-hold workflow, the implanted markers workflow, and for gating tests where remote-controlled movement of a phantom is required. Commissioning tests were all found to be in tolerance, with maximum translational and rotational deviations in SGRT of 0.3 mm and 0.4°, respectively, and X-ray image fusion reproducibility standard deviation of 0.08 mm. Tolerances were based on published documents and upon the performance characteristics of the system as specified by the vendor. The unique configuration of ExacTrac Dynamic requires the end user to design commissioning tests that validate the system for use in the clinical implementation adopted in the department. As there are multiple customizable workflows available, tests should be designed around these workflows, and can be ongoing as workflows are progressively introduced into departmental procedures.
Comparison of Three Commercial Methods of Cone-Beam Computed Tomography-Based Dosimetric Analysis of Head-and-Neck Patients with Weight Loss
Authors: Rathee Satyapal , Burke Benjamin , Heikal Amr
Published: January 2023

Purpose:

This investigation compares three commercial methods of cone-beam computed tomography (CBCT)-based dosimetric analysis to a method based on repeat computed tomography (CT).

Materials and Methods:

Seventeen head-and-neck patients treated in 2020, and with a repeat CT, were included in the analyses. The planning CT was deformed to anatomy in repeat CT to generate a reference plan. Two of the CBCT-based methods generated test plans by deforming the planning CT to CBCT of fraction N using VelocityAI™ and SmartAdapt®. The third method compared directly calculated doses on the CBCT for fraction 1 and fraction N, using PerFraction™. Maximum dose to spinal cord (Cord_dmax) and dose to 95% volume (D95) of planning target volumes (PTVs) were used to assess “need to replan” criteria.

Results:

The VelocityAI™ method provided results that most accurately matched the reference plan in “need to replan” criteria using either Cord_dmax or PTV D95. SmartAdapt® method overestimated the change in Cord_dmax (6.77% vs. 3.85%, P < 0.01) and change in cord volume (9.56% vs. 0.67%, P < 0.01) resulting in increased false positives in “need to replan” criteria, and performed similarly to VelocityAI™ for D95, but yielded more false negatives. PerFraction™ method underestimated Cord_dmax, did not perform any volume deformation, and missed all “need to replan” cases based on cord dose. It also yielded high false negatives using the D95 PTV criteria.

Conclusions:

The VelocityAI™-based method using fraction N CBCT is most similar to the reference plan using repeat CT; the other two methods had significant differences.
Does Fluence Smoothing Reduce the Complexity of the Intensity-Modulated Radiation Therapy Treatment Plan? A Dosimetric Analysis
Authors: Saroj Dinesh Kumar , Yadav Suresh , Paliwal Neetu
Published: January 2023

Background:

Intensity-modulated radiation therapy (IMRT) may have too many peaks and valleys, making the treatment plan undeliverable. When there are too many fluency differences between adjacent pixels in the X or Y directions, the X and Y smoothing factors are utilized as weighting factors to penalize this behavior. Generally, a high degree of complexity is accompanied by many monitor units (MUs), large number of segments, small sized segments, and complex segment shapes. The degree of plan delivery uncertainty can all increase with a higher detailed fluence map.

Aim:

This study aims to evaluate the dosimetric effects of various smoothing levels on the planning target volume (PTV) and organs at risk (OARs) for cervix cancer.

Materials and Methods:

IMRT treatment plans were re-optimized by combining several values of the X and Y penalty between 0 and 100. The dose–volume histogram assessed various dosimetric indicators for PTV and OARs. Additionally, gamma passing rates were evaluated and noted as an indicator of the complex treatment plan.

Results:

At X = 60, Y = 60 fluence map penalty, the conformity index (CI) value reached its highest value of 0.996 ± 0.004. At X = 0, Y = 0, the homogeneity index (HI) was determined to have a maximum value of 0.0628 ± 0.0235. The highest and lowest MU values were 2424.30 ± 471.12 and 1087.80 ± 91.57, respectively, with X = 0, Y = 0 and X = 100, Y = 100. At X = 100, Y = 100, the gamma passing rate reaches its highest value of 99.28% ± 0.44% and minimum value of 85.93% ± 3.87% at X = 0, Y = 0.

Conclusion:

The CI and HI values showed no discernible fluctuation, and the OAR doses were barely affected as smoothing was increased. When the smoothing factor was raised, the number of MUs sharply dropped, and a decrease in the number of segments and higher gamma passing rates were also seen.
Extensions of stable $C^*$-algebras
Authors: Røordam Mikael
Published: January 2023

We show that an extension of two stable

C^*

-algebras need not be stable. More explicitly we find an extension

0 \to C(Z) \otimes {\cal K} \to A \to {\cal K} \to 0

for some (infinite dimensional) compact Hausdorff space

Z

such that

A

is not stable. The

C^*

-algebra

A

in our example has an approximate unit consisting of projections.
Compactification of the Bruhat-Tits building of PGL by lattices of smaller rank.
Authors: Werner Annette
Published: January 2023

In this paper we construct a compactification of the Bruhat-Tits building associated to the group

PGL(V)

by attaching all the Bruhat-Tits buildings of

PGL(W)

for non-trivial subspaces

W

of

V

as a boundary.
Realizing countable groups as automorphism groups of Riemann surfaces
Authors: Winkelmann Jörg
Published: January 2023

Every countable group can be realized as the full automorphism group of a Riemann surface as well as the full group of isometries of a Riemannian manifold.
Divisible subgroups of Brauer groups and trace forms of central simple algebras
Authors: Berhuy Grégory , Leep David B.
Published: January 2023

Let

F

be a field of characteristic different from 2 and assume that

F

satisfies the strong approximation theorem on orderings (

F

is a SAP field) and that

I^3(F)

is torsion-free. We prove that the 2-primary component of the torsion subgroup of the Brauer group of

F

is a divisible group and we prove a structure theorem on the 2-primary component of the Brauer group of

F

. This result generalizes well-known results for algebraic number fields. We apply these results to characterize the trace form of a central simple algebra over such a field in terms of its determinant and signatures.
A generalization of Mumford's geometric invariant theory
Authors: Hausen Jürgen
Published: January 2023

We generalize Mumford's construction of good quotients for reductive group actions. Replacing a single linearized invertible sheaf with a certain group of sheaves, we obtain a Geometric Invariant Theory producing not only the quasiprojective quotient spaces, but more generally all divisorial ones. As an application, we characterize in terms of the Weyl group of a maximal torus, when a proper reductive group action on a smooth complex variety admits an algebraic variety as orbit space.
Planar graphs as minimal resolutions of trivariate monomial ideals
Authors: Miller Ezra
Published: January 2023

We introduce the notion of rigid embedding in a grid surface, a new kind of plane drawing for simple triconnected planar graphs. Rigid embeddings provide methods to (1) find well-structured (cellular, here) minimal free resolutions for arbitrary monomial ideals in three variables; (2) strengthen the Brightwell–Trotter bound on the order dimension of triconnected planar maps by giving a geometric reformulation; and (3) generalize Schnyder's angle coloring of planar triangulations to arbitrary triconnected planar maps via geometry. The notion of rigid embedding is stable under duality for planar maps, and has certain uniqueness properties.
The ground state energy of relativistic one-electron atoms according to Jansen and Heß
Authors: Brummelhuis Raymond , Siedentop Heinz , Stockmeyer Edgardo
Published: January 2023

Jansen and Heß – correcting an earlier paper of Douglas and Kroll – have derived a (pseudo-)relativistic energy expression which is very successful in describing heavy atoms. It is an approximate no-pair Hamiltonian in the Furry picture. We show that their energy in the one-particle Coulomb case, and thus the resulting self-adjoint Hamiltonian and its spectrum, is bounded from below for

\alpha Z\leq 1.006

.
Asymptotics of complete Kähler-Einstein metrics -- negativity of the holomorphic sectional curvature
Authors: Schumacher Georg
Published: January 2023

We consider complete Kähler-Einstein metrics on the complements of smooth divisors in projective manifolds. The estimates proven earlier by the author citeframas imply that in directions parallel to the divisor at infinity the metric tensor converges to the Kähler-Einstein metric on the divisor. Here we show that the holomorphic sectional curvature is bounded from above by a negative constant near infinity.
Hasse invariant and group cohomology
Authors: Edixhoven Bas , Khare Chandrashekhar
Published: January 2023

Let

p\geq5

be a prime number. The Hasse invariant is a modular form modulo

p

that is often used to produce congruences between modular forms of different weights. We show how to produce such congruences between eigenforms of weights 2 and

p+1

, in terms of group cohomology. We also illustrate how our method works for inert primes

p\geq5

in the contexts of quadratic imaginary fields (where there is no Hasse invariant available) and Hilbert modular forms over totally real fields, cyclic and of even degree over the rationals.
A lambda-graph system for the Dyck shift and its $K$-groups
Authors: Krieger Wolfgang , Matsumoto Kengo
Published: January 2023

A property of subshifts is described that allows to associate to the subshift a distinguishied presentation by a compact Shannon graph. For subshifts with this property and for the resulting invariantly associated compact Shannon graphs and their

\lambda

-graph systems the term

\lq

Cantor horizon

\rq

is proposed. The Dyck shifts are Cantor horizon. The

C^*

-algebras that are obtained from the Cantor horizon

\lambda

-graph systems of the Dyck shifts are separable, unital, nuclear, purely infinite and simple with UCT. The K-groups and Bowen-Franks groups of the Cantor horizon

\lambda

-graph systems of the Dyck shifts are computed and it is found that the

K_0

-groups are not finitely generated.
On the scattering theory of the Laplacian with a periodic boundary condition. I. Existence of wave operators
Authors: Frank Rupert L.
Published: January 2023

We study spectral and scattering properties of the Laplacian

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

in

L_2(\R^2_+)

corresponding to the boundary condition

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

for a wide class of periodic functions

\sigma

. The Floquet decomposition leads to problems on an unbounded cell which are analyzed in detail. We prove that the wave operators

W_\pm(H^{(\sigma)},H^{(0)})

exist.
Classification of holomorphic vector bundles on noncommutative two-tori
Authors: Polishchuk A.
Published: January 2023

We prove that every holomorphic vector bundle on a noncommutative two-torus

T

can be obtained by successive extensions from standard holomorphic bundles considered in [2]. This implies that the category of holomorphic bundles on

T

is equivalent to the heart of a certain

t

-structure on the derived category of coherent sheaves on an elliptic curve.
Moduli of Prym curves
Authors: Ballico Edoardo , Casagrande Cinzia , Fontanari Claudio
Published: January 2023

Here we focus on the compactification of the moduli space of curves of genus

g

together with an unramified double cover, constructed by Arnaud Beauville in order to compactify the Prym mapping. We present an alternative description of it, inspired by the moduli space of spin curves of Maurizio Cornalba, and we discuss in detail its main features, both from a geometrical and a combinatorial point of view.
Additive structure of multiplicative subgroups of fields and Galois theory
Authors: Mahé Louis , Mináč Ján , Smith Tara L.
Published: January 2023

One of the fundamental questions in current field theory, related to Grothendieck's conjecture of birational anabelian geometry, is the investigation of the precise relationship between the Galois theory of fields and the structure of the fields themselves. In this paper we initiate the classification of additive properties of multiplicative subgroups of fields containing all squares, using pro-2-Galois groups of nilpotency class at most 2, and of exponent at most 4. This work extends some powerful methods and techniques from formally real fields to general fields of characteristic not 2.
On connecting orbits of semilinear parabolic equations on $S^1$
Authors: Miyamoto Yasuhito
Published: January 2023

It is well-known that any bounded orbit of semilinear parabolic equations of the form

u_t=u_{xx}+f(u,u_x),\quad x\in S^1={\mathbb R}/{\mathbb Z},\quad t>0,

converges to steady states or rotating waves (non-constant solutions of the form

U(x-ct))

under suitable conditions on

f

. Let

S

be the set of steady states and rotating waves (up to shift). Introducing new concepts – the
clusters
and the
structure
of

S

–, we clarify, to a large extent, the heteroclinic connections within

S

; that is, we study which

u\in S

and

v\in S

are connected heteroclinically and which are not, under various conditions. We also show that

\sharp S\geq N+\sum_{j=1}^N [[\sqrt{(f_u(r_j,0))_+}/(2\pi )]]

where

\{r_j\}_{j=1}^N

is the set of the roots of

f(\,\cdot\, ,0)

and

[[y]]

denotes the largest integer that is strictly smaller than

y

. In paticular, if the above equality holds or if

f

depends only on

u

, the
structure
of

S

completely determines the heteroclinic connections.
The centre of completed group algebras of pro-$p$ groups.
Authors: Ardakov Konstantin
Published: January 2023

We compute the centre of the completed group algebra of an arbitrary countably based pro-

p

group with coefficients in

\mathbb Fp

or

\mathbb Zp

. Some other results are obtained.
Convexity, valuations and Prüfer extensions in real algebra
Authors: Knebusch Manfred , Zhang Digen
Published: January 2023

We analyse the interplay between real valuations, Prüfer extensions and convexity with respect to various preorderings on a given commutative ring. We study all this first in preordered rings in general, then in

f

-rings. Most often Prüfer extensions and real valuations abound whenever a preordering is present. The next logical step, to focus on the more narrow class of real closed rings, is not yet taken, except in some examples.
Cohomology of arithmetic groups with infinite dimensional coefficient spaces
Authors: Deitmar Anton , Hilgert Joachim
Published: January 2023

The cuspidal cohomology groups of arithmetic groups in certain infinite dimensional modules are computed. As a result we get a simultaneous generalization of the Patterson-Conjecture and the Lewis-Correspondence.
Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms
Authors: Michor Peter W. , Mumford David
Published: January 2023

The

L^2

-metric or Fubini-Study metric on the non-linear Grassmannian of all submanifolds of type

M

in a Riemannian manifold

(N,g)

induces geodesic distance 0. We discuss another metric which involves the mean curvature and shows that its geodesic distance is a good topological metric. The vanishing phenomenon for the geodesic distance holds also for all diffeomorphism groups for the

L^2

-metric.
Parametrized braid groups of Chevalley groups.
Authors: Loday Jean-Louis , Stein Michael R.
Published: January 2023

We introduce the notion of a braid group parametrized by a ring, which is defined by generators and relations and based on the geometric idea of painted braids. We show that the parametrized braid group is isomorphic to the semi-direct product of the Steinberg group (of the ring) with the classical braid group. The technical heart of the proof is the Pure Braid Lemma, which asserts that certain elements of the parametrized braid group commute with the pure braid group. This first part treats the case of the root system

A_n

; in the second part we prove a similar theorem for the root system

D_n

.
Time-like isothermic surfaces associated to Grassmannian systems
Authors: Dussan M.P. , Magid M.A.
Published: January 2023

We establish that, as is the case with space-like isothermic surfaces, time-like isothermic surfaces in pseudo-riemannian space

\mathbb R^{n-j,j}

are associated to the

O(n-j+1,j+1)/O(n-j,j)\times O(1,1)

-system.
A common recursion for Laplacians of matroids and shifted simplicial complexes
Authors: Duval Art M.
Published: January 2023

A recursion due to Kook expresses the Laplacian eigenvalues of a matroid

M

in terms of the eigenvalues of its deletion

M-e

and contraction

M/e

by a fixed element

e

, and an error term. We show that this error term is given simply by the Laplacian eigenvalues of the pair

(M-e, M/e)

. We further show that by suitably generalizing deletion and contraction to arbitrary simplicial complexes, the Laplacian eigenvalues of shifted simplicial complexes satisfy this exact same recursion. We show that the class of simplicial complexes satisfying this recursion is closed under a wide variety of natural operations, and that several specializations of this recursion reduce to basic recursions for natural invariants. We also find a simple formula for the Laplacian eigenvalues of an arbitrary pair of shifted complexes in terms of a kind of generalized degree sequence.
Koszul duality and equivariant cohomology
Authors: Franz Matthias
Published: January 2023

Let

G

be a topological group such that its homology 

H(G)

with coefficients in a principal ideal domain 

R

is an exterior algebra, generated in odd degrees. We show that the singular cochain functor carries the duality between

G

-spaces and spaces over 

BG

to the Koszul duality between modules up to homotopy over

H(G)

 and 

H^*(BG)

. This gives in particular a Cartan-type model for the equivariant cohomology of a

G

-space with coefficients in 

R

. As another corollary, we obtain a multiplicative quasi-isomorphism 

C^*(BG)\to H^*(BG)

. A key step in the proof is to show that a differential Hopf algebra is formal in the category of

A_\infty

 algebras provided that it is free over 

R

and its homology an exterior algebra.
Capacity associated to a positive closed current
Authors: Khalifa Dabbek , Fredj Elkhadhra
Published: January 2023

Let

\Omega

be an open set of

\mathbb{C}^n

and

T

be a positive closed current of dimension

p\geq 1

on

\Omega

, we define a capacity associated to

T

by:

C_T(K,\Omega)=C_T(K)=\operatorname{sup} \left\{\int_K{T\wedge(dd^c v)^p,\ v\in \mathrm{psh}(\Omega),\ 0<v<1}\right\}

where

K

is a compact set of

\Omega

. We prove, in the same way as Bedford–Taylor, that a locally bounded plurisubharmonic function is quasi-continuous with respect to

C_T

. In the second part we define the convergence relatively to

C_T

and we prove that if

(u_j)

is a family of locally uniformly bounded plurisubharmonic functions and

u

is a locally bounded plurisubharmonic function such that

u_j \rightarrow u

relatively to

C_T

then

T\wedge (dd^cu_j)^p\rightarrow T\wedge (dd^cu)^p

in the current sense.
On the finiteness of Ш for motives associated to modular forms
Authors: Besser Amnon
Published: January 2023

Let

f

be a modular form of even weight on

\Gamma_0(N)

with associated motive

\mathcal{M}_f

. Let

K

be a quadratic imaginary field satisfying certain standard conditions. We improve a result of Nekovar and prove that if a rational prime

p

is outside a finite set of primes depending only on the form

f

, and if the image of the Heegner cycle associated with

K

in the

p

-adic intermediate Jacobian of

\mathcal{M}_f

is not divisible by

p

, then the

p

-part of the Tate-shafarevic group of

\mathcal{M}_f

over

K

is trivial. An important ingredient of this work is an analysis of the behavior of “Kolyvagin test classes” at primes dividing the level

N

. In addition, certain complications, due to the possibility of

f

having a Galois conjugate self-twist, have to be dealt with.
Motivic tubular neighborhoods
Authors: Levine Marc
Published: January 2023

We construct motivic versions of the classical tubular neighborhood and the punctured tubular neighborhood, and give applications to the construction of tangential base-points for mixed Tate motives, algebraic gluing of curves with boundary components, and limit motives.
On the structure of Calabi-Yau categories with a cluster tilting subcategory
Authors: Tabuada Gonçalo
Published: January 2023

We prove that for

d\geq 2

, an algebraic

d

-Calabi-Yau triangulated category endowed with a

d

-cluster tilting subcategory is the stable category of a DG category which is perfectly

(d+1)

-Calabi-Yau and carries a non degenerate

t

-structure whose heart has enough projectives.
Rings of integers of type $K(\pi,1)$
Authors: Schmidt Alexander
Published: January 2023

We investigate the Galois group

G_S(p)

of the maximal

p

-extension unramified outside a finite set

S

of primes of a number field in the (tame) case, when no prime dividing

p

is in

S

. We show that the cohomology of

G_S(p)

is 'often' isomorphic to the étale cohomology of the scheme

\mathit{Spec}({\mathcal O}_k \setminus S)

, in particular,

G_S(p)

is of cohomological dimension 2 then.
$\ell$-adic realization of geometric triangular motives. I
Authors: Ivorra Florian
Published: January 2023

In this work, we provide an integral

\ell

-adic realization functor for Voevodsky's triangulated category of geometrical motives over a noetherian separated scheme. Our approach to the realization problem is to study finite correspondences from the Nisnevich and étale local point of view. We set the existence of a local decomposition for finite correspondences which implies the existence of local transfers. This result allows us to provide canonical transfers on the Godement resolution of a Nisnevich sheaf with transfers and then to carry out the construction of the

\ell

-adic realization functor. We also give a moderate

\ell

-adic realization functor in some geometrical situations.
Essential spectrum of multiparticle Brown-Ravenhall operators in external field
Authors: Morozov Sergey
Published: January 2023

The essential spectrum of multiparticle Brown–Ravenhall operators is characterized in terms of two-cluster decompositions for a wide class of external fields and interparticle interactions and for the systems with prescribed symmetries.
Degeneration of polylogarithms and special values of $L$-functions for totally real fields
Authors: Kings Guido
Published: January 2023

The degeneration of the polylogarithm on the universal abelian scheme over a Hilbert modular variety at the boundary is described in terms of (critical) special values of the

L

-function of the totally real field defining the variety. This gives a relation between the polylogarithm on abelian schemes and special values of

L

-functions.
Andreotti-Mayer loci and the Schottky problem
Authors: Ciliberto Ciro , van der Geer Gerard
Published: January 2023

We prove a lower bound for the codimension of the Andreotti-Mayer locus

N_{g,1}

and show that the lower bound is reached only for the hyperelliptic locus in genus 4 and the Jacobian locus in genus 5. In relation with the intersection of the Andreotti-Mayer loci with the boundary of the moduli space

{\mathcal A}_g

we study subvarieties of principally polarized abelian varieties

(B,\Xi)

parametrizing points

b

such that

\Xi

and the translate

\Xi_b

are tangentially degenerate along a variety of a given dimension.
Profinite homotopy theory
Authors: Quick Gereon
Published: January 2023

We construct a model structure on simplicial profinite sets such that the homotopy groups carry a natural profinite structure. This yields a rigid profinite completion functor for spaces and pro-spaces. One motivation is the étale homotopy theory of schemes in which higher profinite étale homotopy groups fit well with the étale fundamental group which is always profinite. We show that the profinite étale topological realization functor is a good object in several respects.
Comparison of spectral sequences involving bifunctors
Authors: Künzer Matthias
Published: January 2023

Suppose given functors

\mathcal{A}\times\mathcal{A}'\xrightarrow{F}\mathcal{B}\xrightarrow{G}\mathcal{C}

between abelian categories, an object

X

in

\mathcal{A}

and an object

X'

in

\mathcal{A}'

such that

F(X,-), F(-,X')

and

G

are left exact, and such that further conditions hold. We show that,

E_1

-terms exempt, the Grothendieck spectral sequence of the composition of

F(X,-)

and

G

evaluated at

X'

is isomorphic to the Grothendieck spectral sequence of the composition of

F(-,X')

and

G

evaluated at

X

. The respective

E_2

-terms are a priori seen to be isomorphic. But instead of trying to compare the differentials and to proceed by induction on the pages, we rather compare the double complexes that give rise to these spectral sequences.
Bivariant $K$-theory for locally convex algebras and the Chern-Connes character
Authors: Cuntz Joachim
Published: January 2023

We present a new construction of a bivariant

K

-functor. The functor can be defined on various categories of topological algebras. The corresponding bivariant theory has a Kasparov product and the other standard properties of

KK

-theory. We study such a theory in detail on a natural category of locally convex algebras and define a bivariant multiplicative character to bivariant periodic cyclic cohomology.
Hecke operators on quasimaps into horospherical varieties
Authors: Gaitsgory Dennis , Nadler David
Published: January 2023

Let

G

be a connected reductive complex algebraic group. This paper and its companion citeGNcombo06 are devoted to the space

Z

of meromorphic quasimaps from a curve into an affine spherical

G

-variety

X

. The space

Z

may be thought of as an algebraic model for the loop space of

X

. The theory we develop associates to

X

a connected reductive complex algebraic subgroup

\check H

of the dual group

\check G

. The construction of

\check H

is via Tannakian formalism: we identify a certain tensor category

Q(Z)

of perverse sheaves on

Z

with the category of finite-dimensional representations of

\check H

. In this paper, we focus on horospherical varieties, a class of varieties closely related to flag varieties. For an affine horospherical

G

-variety

X_{\mathrm{horo}}

, the category

Q(Z_{\mathrm{horo}})

is equivalent to a category of vector spaces graded by a lattice. Thus the associated subgroup

\check H_{\mathrm{horo}}

is a torus. The case of horospherical varieties may be thought of as a simple example, but it also plays a central role in the general theory. To an arbitrary affine spherical

G

-variety

X

, one may associate a horospherical variety

X_{\mathrm{horo}}

. Its associated subgroup

\check H_{\mathrm{horo}}

turns out to be a maximal torus in the subgroup

\check H

associated to

X

.
On the nonexistence of certain morphisms from Grassmannian to Grassmannian in characteristic $0$
Authors: Ramadoss Ajay C.
Published: January 2023

This paper proves some properties of the big Chern classes of a vector bundle on a smooth scheme over a field of characteristic 0. These properties together with the explicit computation of the big Chern classes of universal quotient bundles of Grassmannians are used to prove the main Theorems (Theorems 1,2 and 3) of this paper. The nonexistence certain morphisms between Grassmannians over a field of characteristic 0 follows directly from these theorems. One of our theorems, for instance, states that the higher Adams operations applied to the class of a universal quotient bundle of a Grassmannian that is not a line bundle yield elements in the K-ring of the Grassmannian that are not representable as classes of genuine vector bundles. This is not true for Grassmannians over a field of characteristic

p

.
Spectral analysis of relativistic atoms – interaction with the quantized radiation field
Authors: Huber Matthias
Published: January 2023

This is the the second part of a series of two papers, which investigate spectral properties of Dirac operators with singular potentials. We will provide a spectral analysis of a relativistic one-electron atom in interaction with the second quantized radiation field and thus extend the work of Bach, Fröhlich, and Sigal [5] and Hasler, Herbst, and Huber[19] to such systems. In particular, we show that the lifetime of excited states in a relativistic hydrogen atom coincides with the life time given by Fermi’s Golden Rule in the non-relativistic case. We will rely on the technical preparations derived in the first part [25] of this work.
Erratum for: “On the parity of ranks of Selmer groups. III” [cf. Documenta Math. 12 (2007), 243–274]
Authors: Nekovář Jan
Published: January 2023

In the manuscript “On the Parity of Ranks of Selmer Groups III” Documenta Math. 12 (2007), 243–274, [1], Remark 4.

1.2(4)

and the treatment of archimedean

\varepsilon

-factors in 4.1.3 are incorrect. Contrary to what is stated in 0.3, the individual archimedean

\varepsilon

-factors

\varepsilon_u(M) (u\mid\infty)

cannot be expressed, in general, in terms of

M_{\mathfrak{p}}

, but their product can.
Equivariant counts of points of the moduli spaces of pointed hyperelliptic curves
Authors: Bergström Jonas
Published: January 2023

We consider the moduli space

\mathcal H_{g,n}

of

n

-pointed smooth hyperelliptic curves of genus

g

. In order to get cohomological information we wish to make

\mathbb S_n

-equivariant counts of the numbers of points defined over finite fields of this moduli space. We find recurrence relations in the genus that these numbers fulfil. Thus, if we can make

\mathbb S_n

-equivariant counts of

\mathcal H_{g,n}

for low genus, then we can do this for every genus. Information about curves of genus 0 and 1 is then found to be sufficient to compute the answers for

\mathcal H_{g,n}

for all

g

and for

n \leq 7

. These results are applied to the moduli spaces of stable curves of genus 2 with up to 7 points, and this gives us the

\mathbb S_n

-equivariant Galois (resp. Hodge) structure of their

\ell

-adic (resp. Betti) cohomology.
Galois representations and Lubin-Tate groups
Authors: Kisin Mark , Ren Wei
Published: January 2023

Using Lubin-Tate groups, we develop a variant of Fontaine's theory of

(\varphi, \Gamma)

-modules, and we use it to give a description of the Galois stable lattices inside certain crystalline representations.
Function fields of one variable over PAC fields
Authors: Jarden Moshe , Pop Florian
Published: January 2023

We give evidence for a conjecture of Serre and a conjecture of Bogomolov.
Thom spectra that are symmetric spectra
Authors: Schlichtkrull Christian
Published: January 2023

We analyze the functorial and multiplicative properties of the Thom spectrum functor in the setting of symmetric spectra and we establish the relevant homotopy invariance.
Hicas of length $\le 4$.
Authors: Miemietz Vanessa , Turner Will
Published: January 2023

A hica is a highest weight, homogeneous, indecomposable, Calabi–Yau category of dimension 0. A hica has length

l

if its objects have Loewy length

l

and smaller. We classify hicas of length

\leq 4

, up to equivalence, and study their properties. Over a fixed field

F

, we prove that hicas of length 4 are in one-one correspondence with bipartite graphs. We prove that an algebra

A_\Gamma

controlling the hica associated to a bipartite graph

\Gamma

is Koszul, if and only if

\Gamma

is not a simply laced Dynkin graph, if and only if the quadratic dual of

A_\Gamma

is Calabi–Yau of dimension 3.
Blow-up of solutions to a periodic nonlinear dispersive rod equation
Authors: Jin Liangbing , Liu Yongming , Zhou Yong
Published: January 2023

In this paper, firstly we find an optimal constant for a convolution problem on the unit circle via the variational method. Then by using the optimal constant, we give a new and improved sufficient condition on the initial data to guarantee the corresponding strong solution blows up in finite time. We also analyze the corresponding ordinary difference equation associate to the convolution problem and give numerical simulation for the optimal constant.
Twisted Pfister forms
Authors: Hoffmann Detlev W.
Published: January 2023

Let

F

be a field of characteristic

\neq 2

. In this paper we investigate quadratic forms

\varphi

over

F

which are anisotropic and of dimension

2^n, n\geq 2

, such that in the Witt ring

WF

they can be written in the form

\varphi=\sigma -\pi

where

\sigma

and

\pi

are anisotropic

n

- resp. 

m

-fold Pfister forms,

1\leq m <n

. We call these forms twisted Pfister forms. Forms of this type with

m=n-1

are of great importance in the study of so-called good forms of height 2, and such forms with

m=1

also appear in Izhboldin's recent proof of the existence of

n

-fold Pfister forms

\tau

over suitable fields

F, n\geq 3

, for which the function field

F(\tau )

is not excellent over

F

. We first derive some elementary properties and try to give alternative characterizations of twisted Pfister forms. We also compute the Witt kernel

W(F(\varphi )/F)

of a twisted Pfister form

\varphi

. Our main focus, however, will be the study of the following problems: For which forms

\psi

does a twisted Pfister form

\varphi

become isotropic over

F(\psi )

? Which forms

\psi

are equivalent to

\varphi

(i.e., the function fields

F(\varphi)

and

F(\psi )

are place-equivalent over

F

)? We also investigate how such twisted Pfister forms behave over the function field of a Pfister form of the same dimension which then leads to a generalization of the result of Izhboldin mentioned above.
Higher index theorems and the boundary map in cyclic cohomology
Authors: Nistor Victor
Published: January 2023

We show that the Chern–Connes character induces a natural transformation from the six term exact sequence in (lower) algebraic

K

-Theory to the periodic cyclic homology exact sequence obtained by Cuntz and Quillen, and we argue that this amounts to a general “higher index theorem.” In order to compute the boundary map of the periodic cyclic cohomology exact sequence, we show that it satisfies properties similar to the properties satisfied by the boundary map of the singular cohomology long exact sequence. As an application, we obtain a new proof of the Connes–Moscovici index theorem for coverings.
The critical values of generalizations of the Hurwitz zeta function
Authors: Shimura Goro
Published: January 2023

We investigate a few types of generalizations of the Hurwitz zeta function, written

Z(s,a)

in this abstract, where

s

is a complex variable and

a

is a parameter in the domain that depends on the type. In the easiest case we take

a\in\mathbf R,

and one of our main results is that

Z(-m,a)

is a constant times

E_m(a)

for

0\le m\in\mathbf Z,

where

E_m

is the generalized Euler polynomial of degree

n.

In another case,

a

is a positive definite real symmetric matrix of size

n,

and

Z(-m,a)

for

0\le m\in\mathbf Z

is a polynomial function of the entries of

a

of degree

\le mn.

We will also define

Z

with a totally real number field as the base field, and will show that

Z(-m,a)\in\mathbf Q

in a typical case.
Locally well generated homotopy categories of complexes
Authors: Stovicek Jan
Published: January 2023

We show that the homotopy category of complexes

\mathbf{K}(\mathcal{B})

over any finitely accessible additive category

\mathcal{B}

is locally well generated. That is, any localizing subcategory

\mathcal{L}

in

\mathbf{K}(\mathcal{B})

which is generated by a set is well generated in the sense of Neeman. We also show that

\mathbf{K}(\mathcal{B})

itself being well generated is equivalent to

\mathcal{B}

being pure semisimple, a concept which naturally generalizes right pure semisimplicity of a ring

R

for

\mathcal{B}= \textrm{Mod-}R

.
Interface and mixed boundary value problems on $n$-dimensional polyhedral domains
Authors: Bacuta C. , Mazzucato A.L. , Nistor V. , Zikatanov L.
Published: January 2023

Let

\mu \in \mathbb Z_+

be arbitrary. We prove a well-posedness result for mixed boundary value/interface problems of second-order, positive, strongly elliptic operators in weighted Sobolev spaces

\mathcal K^m_a(\Omega)

on a bounded, curvilinear polyhedral domain

\Omega

in a manifold

M

of dimension

n

. The typical weight

\eta

that we consider is the (smoothed) distance to the set of singular boundary points of

\partial \Omega

. Our model problem is

Pu:= - \mathrm{div}(A \nabla u) = f

, in

\Omega, u = 0

on

\partial_D \Omega

, and

D^P_\nu u = 0

on

\partial_\nu \Omega

, where the function

A \ge \epsilon > 0

is piece-wise smooth on the polyhedral decomposition

\bar\Omega = \cup_j \bar\Omega_j

, and

\partial \Omega = \partial_D \Omega \cup \partial_N \Omega

is a decomposition of the boundary into polyhedral subsets corresponding, respectively, to Dirichlet and Neumann boundary conditions. If there are no interfaces and no adjacent faces with Neumann boundary conditions, our main result gives an isomorphism

P : \mathcal K^{\mu+1}_{a+1}(\Omega) \cap \{u=0

on

\partial_D \Omega, \ D_\nu^P u=0

on

\partial_N \Omega\} \to \mathcal K^{\mu-1}_{a-1}(\Omega)

for

\mu \ge 0

and

|a|<\eta

, for some

\eta>0

that depends on

\Omega

and

P

but not on

\mu

. If interfaces are present, then we only obtain regularity on each subdomain

\Omega_j

. Unlike in the case of the usual Sobolev spaces,

\mu

can be arbitrarily large, which is useful in certain applications. An important step in our proof is a
regularity
result, which holds for general strongly elliptic operators that are not necessarily positive. The regularity result is based, in turn, on a study of the geometry of our polyhedral domain when endowed with the metric

(dx/\eta)^2

, where

\eta

is the weight (the smoothed distance to the singular set). The well-posedness result applies to positive operators, provided the interfaces are smooth and there are no adjacent faces with Neumann boundary conditions.
The rank-one limit of the Fourier-Mukai transform
Authors: van der Geer Gerard , Kouvidakis Alexis
Published: January 2023

We give a formula for the specialization of the Fourier-Mukai transform on a semi-abelian variety of torus rank 1.
Special subvarieties arising from families of cyclic covers of the projective line
Authors: Moonen Ben
Published: January 2023

We consider families of cyclic covers of

\Bbb P^1

, where we fix the covering group and the local monodromies and we vary the branch points. We prove that there are precisely twenty such families that give rise to a special subvariety in the moduli space of abelian varieties. Our proof uses techniques in mixed characteristics due to Dwork and Ogus.
Inheriting the anti-Specker property
Authors: Bridges Douglas S.
Published: January 2023

The antithesis of Specker's theorem from recursive analysis is further examined from Bishop's constructive viewpoint, with particular attention to its passage to subspaces and products. Ishihara's principle BD-

\mathbf N

comes into play in the discussion of products with the anti-Specker property.
A Lefschetz fixed point formula for singular arithmetic schemes with smooth generic fibres
Authors: Tang Shun
Published: January 2023

In this article, we consider singular equivariant arithmetic schemes whose generic fibres are smooth. For such schemes, we prove a relative fixed point formula of Lefschetz type in the context of Arakelov geometry. This formula is an analog, in the arithmetic case, of the Lefschetz formula proved by R. W. Thomason in [31]. In particular, our result implies a fixed point formula which was conjectured by V. Maillot and D. Rössler in [25].
Log-growth filtration and Frobenius slope filtration of $F$-isocrystals at the generic and special points
Authors: Chiarellotto B. , Tsuzuki N.
Published: January 2023

We study, locally on a curve of characteristic

p >0

, the relation between the log-growth filtration and the Frobenius slope filtration for

F

-isocrystals, which we will indicate as

\varphi-\nabla

-modules, both at the generic point and at the special point. We prove that a bounded

\varphi-\nabla

-module at the generic point is a direct sum of pure

\varphi-\nabla

-modules. By this splitting of Frobenius slope filtration for bounded modules we will introduce a filtration for

\varphi-\nabla

-modules (PBQ filtration). We solve our conjectures of comparison of the log-growth filtration and the Frobenius slope filtration at the special point for particular

\varphi-\nabla

-modules (HPBQ modules). Moreover we prove the analogous comparison conjecture for PBQ modules at the generic point. These comparison conjectures were stated in our previous work citeCT09. Using PBQ filtrations for

\varphi-\nabla

-modules, we conclude that our conjecture of comparison of the log-growth filtration and the Frobenius slope filtration at the special point implies Dwork's conjecture, that is, the special log-growth polygon is above the generic log-growth polygon including the coincidence of both end points.
Ergodic properties and KMS conditions on $C^*$-symbolic dynamical systems
Authors: Matsumoto Kengo
Published: January 2023

A

C^*

-symbolic dynamical system

({\mathcal A}, \rho, \Sigma)

consists of a unital

C^*

-algebra

{\mathcal A}

and a finite family

{ \rho_\alpha }_{\alpha \in \Sigma}

of endomorphisms

\rho_\alpha

of

{\mathcal A}

indexed by symbols

\alpha

of

\Sigma

satisfying some conditions. The endomorphisms

\rho_\alpha, \alpha \in \Sigma

yield both a subshift

\Lambda_\rho

and a

C^*

-algebra

{\mathcal O}_\rho

. We will study ergodic properties of the positive operator

lambda_\rho = \sum_{\alpha \in \Sigma}\rho_\alpha

on

{\mathcal A}

. We will next introduce KMS conditions for continuous linear functionals on

{\mathcal O}_\rho

under gauge action at inverse temperature taking its value in complex numbers. We will study relationships among the eigenvectors of

lambda_\rho

in

{\mathcal A}^*

, the continuous linear functionals on

{\mathcal O}_\rho

satisfying KMS conditions and the invariant measures on the associated one-sided shifts. We will finally present several examples of continuous linear functionals satisfying KMS conditions.
The classification of real purely infinite simple C*-algebras
Authors: Boersema Jeffrey L. , Ruiz Efren , Stacey P.J.
Published: January 2023

We classify real Kirchberg algebras using united

K

-theory. Precisely, let

A

and

B

be real simple separable nuclear purely infinite C*-algebras that satisfy the universal coefficient theorem such that

A_{\mathbb{C}}

and

B_{\mathbb{C}}

are also simple. In the stable case,

A

and

B

are isomorphic if and only if

K^{CRT}(A) \cong K^{CRT}(B)

. In the unital case,

A

and

B

are isomorphic if and only if

(K^{CRT}(A), [1_A]) \cong (K^{CRT}(B), [1_B])

. We also prove that the complexification of such a real C*-algebra is purely infinite, resolving a question left open from [43]. Thus the real C*-algebras classified here are exactly those real C*-algebras whose complexification falls under the classification result of Kirchberg [26] and Phillips[35]. As an application, we find all real forms of the complex Cuntz algebras

{\mathcal{O}}_n

for

2 \leq n \leq \infty

.
K-homology class of the Dirac operator on a compact quantum group
Authors: Neshveyev Sergey , Tuset Lars
Published: January 2023

By a result of Nagy, the C^*-algebra of continuous functions on the

q

-deformation

G_q

of a simply connected semisimple compact Lie group

G

is KK-equivalent to

C(G)

. We show that under this equivalence the K-homology class of the Dirac operator on

G_q

, which we constructed in an earlier paper, corresponds to that of the classical Dirac operator. Along the way we prove that for an appropriate choice of isomorphisms between completions of

U_q\mathfrak g

and

U\mathfrak g

a family of Drinfeld twists relating the deformed and classical coproducts can be chosen to be continuous in

q

.
Stable cohomology of the universal Picard varieties and the extended mapping class group
Authors: Ebert Johannes , Randal-Williams Oscar
Published: January 2023

We study the moduli spaces which classify smooth surfaces along with a complex line bundle. There are homological stability and Madsen–Weiss type results for these spaces (mostly due to Cohen and Madsen), and we discuss the cohomological calculations which may be deduced from them. We then relate these spaces to (a generalisation of) Kawazumi's extended mapping class groups, and hence deduce cohomological information about these. Finally, we relate these results to complex algebraic geometry. We construct a holomorphic stack classifying families of Riemann surfaces equipped with a fibrewise holomorphic line bundle, which is a gerbe over the universal Picard variety, and compute its holomorphic Picard group.
The unirationality of Hurwitz spaces of 6-gonal curves of small genus
Authors: Geiß Florian
Published: January 2023

In this short note we prove the unirationality of Hurwitz spaces of 6-gonal curves of genus

g

with

5\leq g\leq 28

or

g=30,31,35,36,40,45

. Key ingredient is a liaison construction in

\mathbb P^1 \times \mathbb P^2

. By semicontinuity, the proof of the dominance of this construction is reduced to a computation of a single curve over a finite field.
A root space decomposition for finite vertex algebras
Authors: D'Andrea A. , Marchei G.
Published: January 2023

Let

L

be a Lie pseudoalgebra,

a \in L

. We show that, if

a

generates a (finite) solvable subalgebra

S = \langle a \rangle \subset L

, then one may find a lifting

\bar a \in S

of

[a] \in S/S'

such that

\langle \bar a \rangle

is nilpotent.

We then apply this result towards vertex algebras: we show that every finite vertex algebra

V

admits a decomposition into a semi-direct product

V = U ⋉ N

, where

U

is a subalgebra of

V

whose underlying Lie conformal algebra

U^{Lie}

is a nilpotent self-normalizing subalgebra of

V^{Lie}

, and

N = V^{[\infty]}

is a canonically determined ideal contained in the nilradical

\operatorname{Nil} V

.
Several variables $p$-adic $L$-functions for Hida families of Hilbert modular forms
Authors: Ochiai Tadashi
Published: January 2023

After formulating Conjecture A for

p

-adic

L

-functions defined over ordinary Hilbert modular Hida deformations on a totally real field

F

of degree

d

, we construct two

p

-adic

L

-functions of

d+1

-variable depending on the parity of weight as a partial result on Conjecture A. We will also state Conjecture B which is a corollary of Conjecture A but is important by itself. Main issues of the construction are the study of Hida theory of Hilbert modular forms by using Hilbert modular varieties (without using Shimura curves), the study of higher dimensional modular symbols on Hilbert modular varieties and delicate treatments on archimedean and

p

-adic periods.