bluuebunny/crossref_metadata_2025 huggingface dataset:
On Derived Equivalences of K3 Surfaces in Positive Characteristic
Authors: Srivastava Tanya Kaushal
Published: January 2023

For an ordinary K3 surface over an algebraically closed field of positive characteristic we show that every automorphism lifts to characteristic zero. Moreover, we show that the Fourier-Mukai partners of an ordinary K3 surface are in one-to-one correspondence with the Fourier-Mukai partners of the geometric generic fiber of its canonical lift. We also prove that the explicit counting formula for Fourier-Mukai partners of the K3 surfaces with Picard rank two and with discriminant equal to minus of a prime number, in terms of the class number of the prime, holds over a field of positive characteristic as well. We show that the image of the derived autoequivalence group of a K3 surface of finite height in the group of isometries of its crystalline cohomology has index at least two. Moreover, we provide a conditional upper bound on the kernel of this natural cohomological descent map. Further, we give an extended remark in the appendix on the possibility of an F-crystal structure on the crystalline cohomology of a K3 surface over an algebraically closed field of positive characteristic and show that the naive F-crystal structure fails in being compatible with inner product.
Tree Normal Forms for Quiver Representations
Authors: Kinser Ryan , Weist Thorsten
Published: January 2023

We explore methods for constructing normal forms of indecomposable quiver representations. The first part of the paper develops homological tools for recursively constructing families of indecomposable representations from indecomposables of smaller dimension vector. This is then specialized to the situation of tree modules, where the existence of a special basis simplifies computations and gives nicer normal forms. Motivated by a conjecture of Kac, we use this to construct cells of indecomposable representations as deformations of tree modules. The second part of the paper develops geometric tools for constructing cells of indecomposable representations from torus actions on moduli spaces of representations. As an application, we combine these methods to construct families of indecomposables grouped into cells. These actually give a normal form for all indecomposables of certain roots.
Polarized Relations on Horizontal $\operatorname{SL}(2)$'s
Authors: Kerr Matt , Pearlstein Gregory J. , Robles Colleen
Published: January 2023

We introduce a relation on real conjugacy classes of

\operatorname{SL}(2)

-orbits in a Mumford-Tate domain

D

. The relation answers the question when is one

\mathbb{R}

-split polarized mixed Hodge structure more singular/degenerate than another?. The relation is compatible with natural partial orders on the sets of nilpotent orbits in the corresponding Lie algebra and boundary orbits in the compact dual.

A generalization of the

\operatorname{SL}(2)

-orbit theorem to such domains leads to an algorithm for computing this relation. The relation is then worked out in several examples and special cases, including period domains, Hermitian symmetric domains, and complete flag domains.

Although the above relation is not in general a partial order, it leads (via cubical sets) to a poset of equivalence classes of multivariable nilpotent orbits on

D

. The elements of this poset encode the possible degeneracy relations amongst the polarized mixed Hodge structures that arise in a several-variable degeneration of Hodge structure. We conclude with an example illustrating a link to mirror symmetry for Calabi-Yau VHS.
Erratum for “The Dirac Operator with Mass $m_0 \geq 0$: Non-Existence of Zero Modes and of Threshold Eigenvalues”
Authors: Kalf Hubert , Okaji Takashi , Yamada Osanobu
Published: January 2023

We give a proof of Theorem 2.1 in [
H. Kalf
et al., Doc. Math. 20, 37–64 (2015; Zbl 1333.35227)], namely of the following assertion.

Let

Q \colon \mathbb{R}^n \rightarrow \mathbb{C}^{N\times N}

be measurable with

\sup_{x \in \mathbb{R}^n} |x||Q(x)| \leq C \ \ \text{ for some}\ \ 0<C<\frac{n-1}{2}.

Then any solution

u \in H_{\text{loc}}^1(\mathbb{R}^n)^N \cap L^2(\mathbb{R}^n, r^{-1}dx)^N

of

(\alpha\cdot p +Q)u=0

is identically zero.
$K$-Theory of Non-Archimedean Rings. I
Authors: Kerz Moritz , Saito Shuji , Tamme Georg
Published: January 2023

We introduce a variant of homotopy

K

-theory for Tate rings, which we call

analytic

K

-theory

. It is homotopy invariant with respect to the analytic affine line viewed as an ind-object of closed disks of increasing radii. Under a certain regularity assumption we prove an analytic analog of the Bass fundamental theorem and we compare analytic

K

-theory with continuous

K

-theory, which is defined in terms of models. Along the way we also prove some results about the algebraic

K

-theory of Tate rings.
Non-Commutative $L$-Functions for $p$-Adic Representations over Totally Real Fields
Authors: Witte Malte
Published: January 2023

We prove a unicity result for the non-commutative

L

-functions for

p

-adic representations over totally real fields-functions appearing in the non-commutative Iwasawa main conjecture over totally real fields. We then consider continuous representations

\rho

of the absolute Galois group of a totally real field

F

on adic rings in the sense of Fukaya and Kato. Using our unicity result, we show that there exists a unique sensible definition of a non-commutative

L

-function for any such

\rho

that factors through the Galois group of a possibly infinite totally real extension. We also consider the case of CM-extensions and discuss the relation with the equivariant main conjecture for realisations of abstract 1-motives of Greither and Popescu.
Subdivisional Spaces and Graph Braid Groups
Authors: An Byung Hee , Drummond-Cole Gabriel C. , Knudsen Ben
Published: January 2023

We study the problem of computing the homology of the configuration spaces of a finite cell complex

X

. We proceed by viewing

X

, together with its subdivisions, as a
subdivisional space
– a kind of diagram object in a category of cell complexes. After developing a version of Morse theory for subdivisional spaces, we decompose

X

and show that the homology of the configuration spaces of

X

is computed by the derived tensor product of the Morse complexes of the pieces of the decomposition, an analogue of the monoidal excision property of factorization homology.

Applying this theory to the configuration spaces of a graph, we recover a cellular chain model due to Swiatkowski. Our method of deriving this model enhances it with various convenient functorialities, exact sequences, and module structures, which we exploit in numerous computations, old and new.
Singular TQFTs, Foams and Type D Arc Algebras
Authors: Ehrig Michael , Tubbenhauer Daniel , Wilbert Arik
Published: January 2023

We combinatorially describe the 2-category of singular cobordisms, called (rank one) foams, which governs the functorial version of Khovanov homology. As an application we topologically realize the type D arc algebra using this singular cobordism construction.
On the Equivariant Cohomology of Hyperpolar Actions on Symmetric Spaces
Authors: Goertsches Oliver , Hagh Shenas Noshari Sam , Mare Augustin-Liviu
Published: January 2023

We show that the equivariant cohomology of any hyperpolar action of a compact and connected Lie group on a symmetric space of compact type is a Cohen-Macaulay ring. This generalizes some results previously obtained by the authors.
Constructible $1$-Motives and Exactness of Realisation Functors
Authors: Lehalleur Simon Pepin
Published: January 2023

The triangulated category of cohomological

1

-motives with rational coefficients over a base scheme admits a motivic t-structure. We prove that this t-structure restricts to the subcategory of compact objects, and that pullbacks along arbitrary morphisms, as well as Betti and étale realisation functors, are t-exact relative to this t-structure. These exactness properties follow from a structural result: compact objects in the heart behave like a constructible sheaf of Deligne

1

-motives.
Degeneration of Intermediate Jacobians and the Torelli Theorem
Authors: Basu Suratno , Dan Ananyo , Kaur Inder
Published: January 2023

Mumford and Newstead generalized the classical Torelli theorem to higher rank, i.e. a smooth, projective curve

X

is uniquely determined by the second intermediate Jacobian of the moduli space of stable rank

2

bundles on

X

, with fixed odd degree determinant. In this article we prove the analogous result in the case

X

is an irreducible nodal curve with one node. As a byproduct, we obtain the degeneration of the second intermediate Jacobians and the associated Néron model of a family of such moduli spaces.
Orbifold Products for Higher $K$-Theory and Motivic Cohomology
Authors: Fu Lie , Nguyen Manh Toan
Published: January 2023

Due to the work of many authors in the last decades, given an algebraic orbifold (smooth proper Deligne-Mumford stack with trivial generic stabilizer), one can construct its orbifold Chow ring and orbifold Grothendieck ring, and relate them by the orbifold Chern character map, generalizing the fundamental work of Chen-Ruan on orbifold cohomology. In this paper, we extend this theory naturally to higher Chow groups and higher algebraic

K

-theory, mainly following the work of Jarvis-Kaufmann-Kimura and Edidin-Jarvis-Kimura.
Coisotropic Triples, Reduction and Classical Limit
Authors: Dippell Marvin , Esposito Chiara , Waldmann Stefan
Published: January 2023

Coisotropic reduction from Poisson geometry and deformation quantization is cast into a general and unifying algebraic framework: we introduce the notion of coisotropic triples of algebras for which a reduction can be defined. This allows to construct also a notion of bimodules for such triples leading to bicategories of bimodules for which we have a reduction functor as well. Morita equivalence of coisotropic triples of algebras is defined as isomorphism in the ambient bicategory and characterized explicitly. Finally, we investigate the classical limit of coisotropic triples of algebras and their bimodules and show that classical limit commutes with reduction in the bicategory sense.
Boardman's Whole-Plane Obstruction Group for Cartan-Eilenberg Systems
Authors: Helle Gard Olav , Rognes John
Published: January 2023

Each extended Cartan-Eilenberg system

(H, \partial)

gives rise to two exact couples and one spectral sequence. We show that the canonical colim-lim interchange morphism associated to

H

is a surjection, and that its kernel is isomorphic to Boardman's whole-plane obstruction group

W

, for each of the two exact couples.
$p$-Adic Tate Conjectures and Abeloid Varieties
Authors: Gregory Oliver , Liedtke Christian
Published: January 2023

We explore Tate-type conjectures over

p

-adic fields, especially a conjecture of
W. Raskind
[in: Algebra and number theory. Proceedings of the silver jubilee conference, Hyderabad, India, December 11–16, 2003. New Delhi: Hindustan Book Agency. 99–115 (2005; Zbl 1085.14009)] that predicts the surjectivity of

(\text{NS}(X_{\overline{K}}) \otimes_{\mathbb{Z}}\mathbb{Q}_p)^{G_{K}}\longrightarrow H_{\text{ét}}^2(X_{\overline{K}},\mathbb{Q}_p(1))^{G_{K}}

if

X

is smooth and projective over a

p

-adic field

K

and has totally degenerate reduction. Sometimes, this is related to

p

-adic uniformisation. For abelian varieties, Raskind's conjecture is equivalent to the question whether

\text{Hom}(A,B)\otimes\mathbb{Q}_p \,\to\, \text{Hom}_{G_{K}}(V_p(A),V_p(B))

is surjective if

A

and

B

are abeloid varieties over a

p

-adic field.

Using

p

-adic Hodge theory and Fontaine's functors, we reformulate both problems into questions about the interplay of

\mathbb{Q}

-versus

\mathbb{Q}_p

-structures inside filtered

(\varphi,N)

-modules. Finally, we disprove all of these conjectures and questions by showing that they can fail for algebraisable abeloid surfaces, that is, for abelian surfaces with totally degenerate reduction.
Pullbacks of Saito-Kurokawa Lifts and a Central Value Formula for Degree 6 $L$-Series
Authors: Pal Aprameyo , de Vera-Piquero Carlos
Published: January 2023

We prove an explicit central value formula for a family of complex

L

-series of degree 6 for

\text{GL}_2 \times \text{GL}_3

which arise as factors of certain Garret-Rankin triple product

L

-series associated with modular forms. Our result generalizes a previous formula of Ichino involving Saito-Kurokawa lifts, and as an application we prove Deligne's conjecture stating the algebraicity of the central values of the considered

L

-series up to the relevant periods.
Quivers with Additive Labelings: Classification and Algebraic Entropy
Authors: Galashin Pavel , Pylyavskyy Pavlo
Published: January 2023

We show that Zamolodchikov dynamics of a recurrent quiver has zero algebraic entropy only if the quiver has a weakly subadditive labeling, and conjecture the converse. By assigning a pair of generalized Cartan matrices of affine type to each quiver with an additive labeling, we completely classify such quivers, obtaining 40 infinite families and 13 exceptional quivers. This completes the program of classifying Zamolodchikov periodic and integrable quivers.
Real Trace Expansions
Authors: Fischer Véronique
Published: January 2023

In this paper, we investigate trace expansions of operators of the form

A\eta(t\mathcal{L})

where

\eta:\mathbb{R}\rightarrow\mathbb{C}

is a Schwartz function,

A

and

\mathcal L

are classical pseudo-differential operators on a compact manifold

M

with

\mathcal L

elliptic. In particular, we show that, under certain hypotheses, this trace admits an expansion in powers of

t\rightarrow 0^+

. We also relate the constant coefficient to the non-commutative residue and the canonical trace of

A

. Our main tool is the continuous inclusion of the functional calculus of

\mathcal{L}

into the pseudo-differential calculus whose proof relies on the Helffer-Sjöstrand formula.
On a motion of a ball in a viscous fluid.
Authors: Hoffmann Karl-Heinz , Starovoitov Victor N.
Published: January 2023

In dieser Arbeit untersuchen wir die Bewegung einer Festkugel im beschränkten Gebiet, das mit einer inkompressiblen zähen Flüssigkeit gefüllt ist. Wir beweisen, dass die Festkugel die Wand des Behälters mit der Geschwindigkeit Null erreicht. Als eine Folgerung wird die Lösbarkeit der Aufgabe gezeigt.
Relative $B$-Groups
Authors: Bouc Serge
Published: January 2023

This paper extends the notion of

B

-group to a relative context. For a finite group

K

and a field

\mathbb{F}

of characteristic 0, the lattice of ideals of the Green biset functor

\mathbb{F}B_K

obtained by shifting the Burnside functor

\mathbb{F}B

by

K

is described in terms of

B_K

-
groups
. It is shown that any finite group

(L,\varphi)

over

K

admits a
largest quotient

B_K

-
group

\beta_K(L,\varphi)

. The simple subquotients of

\mathbb{F}B_K

are parametrized by

B_K

-groups, and their evaluations can be precisely determined. Finally, when

p

is a prime, the restriction

\mathbb{F}B_K^{(p)}

of

\mathbb{F}B_K

to finite

p

-groups is considered, and the structure of the lattice of ideals of the Green functor

\mathbb{F}B_K^{(p)}

is described in full detail. In particular, it is shown that this lattice is always finite.
Tensor Products of Affine and Formal Abelian Groups
Authors: Bauer Tilman , Carlson Magnus
Published: January 2023

In this paper we study tensor products of affine abelian group schemes over a perfect field

k

. We first prove that the tensor product

G_1 \otimes G_2

of two affine abelian group schemes

G_1,G_2

over a perfect field

k

exists. We then describe the multiplicative and unipotent part of the group scheme

G_1 \otimes G_2

. The multiplicative part is described in terms of Galois modules over the absolute Galois group of

k

. We describe the unipotent part of

G_1 \otimes G_2

explicitly, using Dieudonné theory in positive characteristic. We relate these constructions to previously studied tensor products of formal group schemes.
On the Classification of Lie Bialgebras by Cohomological Means
Authors: Alsaody Seidon , Pianzola Arturo
Published: January 2023

We approach the classification of Lie bialgebra structures on simple Lie algebras from the viewpoint of descent and non-abelian cohomology. We achieve a description of the problem in terms of faithfully flat cohomology over an arbitrary ring over

\mathbb{Q}

, and solve it for Drinfeld-Jimbo Lie bialgebras over fields of characteristic zero. We consider the classification up to isomorphism, as opposed to equivalence, and treat split and non-split Lie algebras alike. We moreover give a new interpretation of scalar multiples of Lie bialgebras hitherto studied using twisted Belavin-Drinfeld cohomology.
Projective Superspace Varieties, Superspace Quadrics and Non-Splitting
Authors: Bettadapura Kowshik
Published: January 2023

This article is a continuation of a previous article which concerned the splitting problem for subspaces of superspaces. We begin with a general account of projective superspaces. Subsequently, we specialise to subvarieties of "positive" projective superspaces. Our main result is: positive, projective superspaces are "normal", in a sense we define. Then, among others, our main application is: smooth, non-reduced, superspace quadric hypersurfaces are non-split.
On the Whistle Cobordism Operation in String Topology of Classifying Spaces
Authors: Kuribayashi Katsuhiko
Published: January 2023

In this manuscript, we consider cobordism operations in the

2

-dimensional labeled open-closed topological quantum field theory for the classifying space of a connected compact Lie group in the sense of Guldberg. In particular, it is proved that the whistle cobordism operation is non-trivial in general provided the labels are in the set of maximal closed subgroups of the given Lie group. The non-triviality of cobordism operations induced by gluing the whistle with the opposite and other labeled cobordisms is also discussed.
The Category of Finitely Presented Smooth Mod $p$ Representations of $GL_2(F)$
Authors: Shotton Jack
Published: January 2023

Let

F

be a finite extension of

\mathbb{Q}_p

. We prove that the category of finitely presented smooth

Z

-finite representations of

GL_2(F)

over a finite extension of

\mathbb{F}_p

is an abelian subcategory of the category of all smooth representations. The proof uses amalgamated products of completed group rings.
Rational Models for Automorphisms of Fiber Bundles
Authors: Berglund Alexander
Published: January 2023

Given a fiber bundle, we construct a differential graded Lie algebra model, in the sense of Quillen's rational homotopy theory, for the classifying space of the monoid of homotopy equivalences of the base covered by a fiberwise isomorphism of the total space.
Essential Dimension and Genericity for Quiver Representations
Authors: Scavia Federico
Published: January 2023

We study the essential dimension of representations of a fixed quiver with given dimension vector. We also consider the question of when the genericity property holds, i.e., when essential dimension and generic essential dimension agree. We classify the quivers satisfying the genericity property for every dimension vector and show that for every wild quiver the genericity property holds for infinitely many of its Schur roots. We also construct a large class of examples, where the genericity property fails. Our results are particularly detailed in the case of Kronecker quivers.
A classification theorem for nuclear purely infinite simple $C^*$-algebras
Authors: Phillips N.Christopher
Published: January 2023

Starting from Kirchberg's theorems announced at the operator algebra conference in Genève in 1994, namely

{\cal O}_{2} \otimes A \cong {\cal O}_{2}

for separable unital nuclear simple

A

and

{\cal O}_{\infty} \otimes {A} \cong A

for separable unital nuclear purely infinite simple

A,

we prove that

KK

-equivalence implies isomorphism for nonunital separable nuclear purely infinite simple

C^*

-algebras. It follows that if

A

and

B

are unital separable nuclear purely infinite simple

C^*

-algebras which satisfy the Universal Coefficient Theorem, and if there is a graded isomorphism from

K_* (A)

to

K_* (B)

which preserves the

K_0

-class of the identity, then

A \cong B.
Quantum Affine Wreath Algebras
Authors: Rosso Daniele , Savage Alistair
Published: January 2023

To each symmetric algebra we associate a family of algebras that we call
quantum affine wreath algebras
. These can be viewed both as symmetric algebra deformations of affine Hecke algebras of type

A

and as quantum deformations of affine wreath algebras. We study the structure theory of these new algebras and their natural cyclotomic quotients.
The Well-Posedness of the Cauchy Problem for the Dirac Operator on Globally Hyperbolic Manifolds with Timelike Boundary
Authors: Grosse Nadine , Murro Simone
Published: January 2023

We consider the Dirac operator on globally hyperbolic manifolds with timelike boundary and show well-posedness of the Cauchy initial boundary value problem coupled to MIT-boundary conditions. This is achieved by transforming the problem locally into a symmetric positive hyperbolic system, proving existence and uniqueness of weak solutions and then using local methods developed by Lax, Phillips and Rauch, Massey to show smoothness of the solutions. Our proof actually works for a slightly more general class of local boundary conditions.
A Characterization of Permutation Modules Extending a Theorem of Weiss
Authors: MacQuarrie John William , Zalesskii Pavel
Published: January 2023

Let

G

be a finite

p

-group with normal subgroup

N

. A celebrated theorem of A. Weiss gives a sufficient condition for a

\mathbb{Z}_pG

-lattice to be a permutation module, looking only at its restriction to

N

and its

N

-fixed points. In case

N

has order

p

, we extend the condition of Weiss to a characterization.
Intersection Space Constructible Complexes
Authors: Agustín Vicente Marta , Fernandez de Bobadilla Javier
Published: January 2023

We present an obstruction theoretic inductive construction of intersection space pairs, which generalizes Banagl's construction of intersection spaces for arbitraty depth stratifications. We construct intersection space pairs for pseudomanifolds with compatible trivial structures at the link fibrations; this includes the case of toric varieties. We define intersection space complexes in an axiomatic way, similar to Goresky-McPherson axioms for intersection cohomology. We prove that if the intersection space pair exists, then the pseudomanifold has an intersection space complex whose hypercohomology recovers the cohomology of the intersection space pair. We characterize existence and uniqueness of intersection space complexes in terms of the derived category of constructible complexes. In the case of algebraic varieties we show that a parallel obstruction theory in the derived category of Mixed Hodge Modules endowes intersection space cohomology with a Mixed Hodge Structure if the obstruction vanishes. We find classes of examples admitting intersection space complex, and counterexamples not admitting them which illustrate the use of the previously developed obstruction theory (counterexamples were known previously by various specialists). We prove that the (shifted) Verdier dual of an intersection space complex is an intersection space complex. We prove a generic Poincaré duality theorem for intersection space complexes.
New uncertainty principles for the continuous Gabor transform and the continuous wavelet transform
Authors: Wilczok Elke
Published: January 2023

Gabor and wavelet methods are preferred to classical Fourier methods, whenever the time dependence of the analyzed signal is of the same importance as its frequency dependence. However, there exist strict limits to the maximal time-frequency resolution of these both transforms, similar to Heisenberg's uncertainty principle in Fourier analysis. Results of this type are the subject of the following article. Among else, the following will be shown: if

\psi

is a window function,

f\in L^2({\bf R})\setminus\{0\}

an arbitrary signal and

G_\psi f(\omega,t)

the continuous Gabor transform of

f

with respect to

\psi

, then the support of

G_\psi f(\omega,t)

considered as a subset of the time-frequency-plane

{\bf R}^2

cannot possess finite Lebesgue measure. The proof of this statement, as well as the proof of its wavelet counterpart, relies heavily on the well known fact that the ranges of the continuous transforms are reproducing kernel Hilbert spaces, showing some kind of shift-invariance. The last point prohibits the extension of results of this type to discrete theory.
Aspects of Enumerative Geometry with Quadratic Forms
Authors: Levine Marc
Published: January 2023

Using the motivic stable homotopy category over a field

k

, a smooth variety

X

over

k

has an Euler characteristic

\chi(X/k)

in the Grothendieck-Witt ring

\operatorname{GW}(k)

. The rank of

\chi(X/k)

is the classical

\mathbb{Z}

-valued Euler characteristic, defined using singular cohomology or étale cohomology, and the signature of

\chi(X/k)

under a real embedding

\sigma:k\to \mathbb{R}

gives the topological Euler characteristic of the real points

X^\sigma(\mathbb{R})

.

We develop tools to compute

\chi(X/k)

, assuming

k

has characteristic

\neq 2

and apply these to refine some classical formulas in enumerative geometry, such as formulas for the top Chern class of the dual, symmetric powers and tensor products of bundles, to identities for the Euler classes in Chow-Witt groups. We also refine the classical Riemann-Hurwitz formula to an identity in

\operatorname{GW}(k)

and compute

\chi(X/k)

for hypersurfaces in

\mathbb{P}^{n+1}_k

defined by a polynomial of the form

\sum_{i=0}^{n+1}a_iX_i^m

; this latter includes the case of an arbitrary quadric hypersurface.

This paper is a revision of [
M. Levine
,"Toward an enumerative geometry with quadratic forms", Preprint, ].
Comparison Theory of Distance Spheres along Geodesics
Authors: Brocks Reinhard
Published: January 2023

Estimates for the principal curvature of distance spheres in Riemannian manifolds with sectional curvature bounded from below are well known. The same holds for the mean curvature of distance spheres in Riemannian manifolds with Ricci curvature bounded from below.

In this article we present new estimates for convexity properties of the distance function of a point under different assumptions, for example for manifolds with lower bounds on the conjugate or on the focal radius in addition to these curvature conditions.

The main idea is to introduce a new tensor field describing the differential of the exponential map and verifying a Riccati equation. This technique allows us to get new estimates for the volume form and for Jacobi fields in this context but also to gain new insights into well-known comparison theorems.
Transitions from relative equilibria to relative periodic orbits
Authors: Wulf Claudia
Published: January 2023

We consider

G

-equivariant semilinear parabolic equations where

G

is a finite-dimensional possibly non-compact symmetry group. We treat periodic forcing of relative equilibria and resonant periodic forcing of relative periodic orbits as well as Hopf bifurcation from relative equilibria to relative periodic orbits using Lyapunov-Schmidt reduction. Our main interest are drift phenomena caused by resonance. In comparison to a center manifold approach Lyapunov-Schmidt reduction is technically easier. We discuss impacts of our results on spiral wave dynamics.
Deformation of Multiple Zeta Values and Their Logarithmic Interpretation in Positive Characteristic
Authors: Gezmiş Oğuz
Published: January 2023

Pellarin introduced the deformation of multiple zeta values of Thakur as elements over Tate algebras. In this paper, we relate these values to a certain coordinate of the logarithm of a higher dimensional Drinfeld module over the Tate algebra which we will introduce. Moreover, we define multiple polylogarithms in our setting and represent deformation of multiple zeta values as a linear combination of multiple polylogarithms. As an application of our results, we also write Dirichlet-Goss multiple

L

-values as a linear combination of twisted multiple polylogarithms at algebraic points.
Monodromy for Some Rank Two Galois Representations over CM Fields
Authors: Allen Patrick B. , Newton James
Published: January 2023

We investigate local-global compatibility for cuspidal automorphic representations

\pi

for

\operatorname{GL}_2

over CM fields that are regular algebraic of weight

0

. We prove that for a Dirichlet density one set of primes

l

and any

\iota : \overline{\mathbf{Q}}_l \xrightarrow {\sim} \mathbf{C}

, the

l

-adic Galois representation attached to

\pi

and

\iota

has nontrivial monodromy at any

v\nmid l

in

F

at which

\pi

is special.
The Weak Tracial Rokhlin Property for Finite Group Actions on Simple C*-Algebras
Authors: Forough Marzieh , Golestani Nasser
Published: January 2023

We develop the concept of weak tracial Rokhlin property for finite group actions on simple (not necessarily unital) C*-algebras and study its properties systematically. In particular, we show that this property is stable under restriction to invariant hereditary C*-algebras, minimal tensor products, and direct limits of actions. Some of these results are new even in the unital case and answer open questions asked by N. C. Phillips in full generality. We present several examples of finite group actions with the weak tracial Rokhlin property on simple stably projectionless C*-algebras. We prove that if

\alpha \colon G \rightarrow \text{Aut}(A)

is an action of a finite group

G

on a simple C*-algebra

A

with tracial rank zero and

\alpha

has the weak tracial Rokhlin property, then the crossed product

A \rtimes_{\alpha} G

and the fixed point algebra

A^{\alpha}

are simple with tracial rank zero. This extends a result of N. C. Phillips to the nonunital case. We use the machinery of Cuntz subequivalence to work in this nonunital setting.
Actions, Quotients and Lattices of Locally Compact Quantum Groups
Authors: Brannan Michael , Chirvasitu Alexandru , Viselter Ami
Published: January 2023

We prove a number of property (T) permanence results for locally compact quantum groups under exact sequences and the presence of invariant states, analogous to their classical versions. Along the way we characterize the existence of invariant weights on quantum homogeneous spaces of quotient type, and relate invariant states for LCQG actions on von Neumann algebras to invariant vectors in canonical unitary implementations, providing an application to amenability. Finally, we introduce a notion of lattice in a locally compact quantum group, noting examples provided by Drinfeld doubles of compact quantum groups. We show that property (T) lifts from a lattice to the ambient LCQG, just as it does classically, thus obtaining new examples of non-classical, non-compact, non-discrete LCQGs with property (T).
Iwasawa theory for symmetric squares of non-$p$-ordinary eigenforms
Authors: Büyükboduk Kazim , Lei Antonio , Venkat Guhan
Published: January 2023

Let

f

be a normalized cuspidal eigen-newform of level coprime to

p

with

a_p(f)=0

. We formulate both integral signed Iwasawa main conjectures and analytic Iwasawa main conjectures attached to the symmetric square motive of

f

twisted by an auxiliary Dirichlet character. We show that the Beilinson-Flach elements attached to the symmetric square motive factorize into integral signed Beilinson-Flach elements, giving evidence towards the existence of a rank-two Euler system predicted by Perrin-Riou. We use these integral elements to prove one inclusion in the integral and analytic Iwasawa main conjectures.
$n$-quasi-abelian categories vs $n$-tilting torsion pairs
Authors: Fiorot Luisa
Published: January 2023

It is a well established fact that the notions of quasi-abelian categories and tilting torsion pairs are equivalent. This equivalence fits in a wider picture including tilting pairs of

t

-structures. Firstly, we extend this picture into a hierarchy of

n

-quasi-abelian categories and

n

-tilting torsion classes. We prove that any

n

-quasi-abelian category

\mathcal{E}

admits a "derived" category

D(\mathcal{E})

endowed with a

n

-tilting pair of

t

-structures such that the respective hearts are derived equivalent. Secondly, we describe the hearts of these

t

-structures as quotient categories of coherent functors, generalizing Auslander's Formula. Thirdly, we apply our results to Bridgeland's theory of perverse coherent sheaves for flop contractions. In Bridgeland's work, the relative dimension

1

assumption guaranteed that

f_\ast

-acyclic coherent sheaves form a

1

-tilting torsion class, whose associated heart is derived equivalent to

D(Y)

. We generalize this theorem to relative dimension

2

.
Semistable reduction of modular curves associated with maximal subgroups in prime level
Authors: Edixhoven Bas , Parent Pierre
Published: January 2023

We complete the description of semistable models for modular curves associated with maximal subgroups of

\mathrm{GL}_2 (\mathbb{F}_p )

(for

p

any prime,

p>5)

. That is, in the new cases of non-split Cartan modular curves and exceptional subgroups, we identify the irreducible components and singularities of the reduction

\mathrm{mod}\,\,p

, and the complete local rings at the singularities. We review the case of split Cartan modular curves. This description suffices for computing the group of connected components of the fibre at 

p

of the Néron model of the Jacobian.
Reduced Whitehead groups of prime exponent algebras over $p$-adic curves
Authors: Bhaskhar Nivedita
Published: January 2023

Let

F

be the function field of a curve over a

p

-adic field. Let

D/F

be a central division algebra of prime exponent

\ell

which is different from

p

. Assume that

F

contains a primitive

\ell^{2th}

root of unity. Then the abstract group

\mathrm{SK}_1(D):=\frac{\mathrm{SL}_1(D)}{\left[D^{\ast}, D^{\ast}\right]}

is trivial.
Complete intersections of quadrics and complete intersections on Segre varieties with common specializations
Authors: Peters Chris , Sterk Hans
Published: January 2023

We investigate whether surfaces that are complete intersections of quadrics and complete intersection surfaces in the Segre embedded product

\mathbf{P}^1\times \mathbf{P}^k\hookrightarrow \mathbf{P}^{2k+1}

can belong to the same Hilbert scheme. For

k=2

there is a classical example; it comes from K3 surfaces in projective

5

-space that degenerate into a hypersurface on the Segre threefold. We show that for

k\geq 3

there is only one more example. It turns out that its (connected) Hilbert scheme has at least two irreducible components. We investigate the corresponding local moduli problem.
On the inner Daniell-Stone and Riesz representation theorems
Authors: König Heinz
Published: January 2023

The paper deals with the context of the inner Daniell-Stone and Riesz representation theorems, which arose within the new development in measure and integration in the book 1997 and subsequent work of the author. The theorems extend the traditional ones, in case of the Riesz theorem to arbitrary Hausdorff topological spaces. The extension enforces that the assertions attain different forms. The present paper wants to exhibit special situations in which the theorems retain their familiar appearance.
Algebraic connective $K$-theory of a Severi-Brauer variety with prescribed reduced behavior
Authors: Mackall Eoin
Published: January 2023

We show that Chow groups of low dimension cycles are torsion free for a class of sufficiently generic Severi-Brauer varieties. Using a recent result of Karpenko, this allows us to compute the algebraic connective

K

-theory in low degrees for the same class of varieties. Independently of these results, we show that the associated graded ring for the topological filtration on the Grothendieck ring is torsion free in the same degrees for an arbitrary Severi-Brauer variety.
Morel homotopy modules and Milnor-Witt cycle modules
Authors: Feld Niels
Published: January 2023

We study the cohomology theory and the canonical Milnor-Witt cycle module associated to a motivic spectrum. We prove that the heart of Morel-Voevodsky stable homotopy category over a perfect field (equipped with its homotopy t-structure) is equivalent to the category of Milnor-Witt cycle modules, thus generalising Déglise's thesis. As a corollary, we recover a theorem of Ananyevskiy and Neshitov, and we prove that the Milnor-Witt K-theory groups are birational invariants.
Torsors of isotropic reductive groups over Laurent polynomials
Authors: Stavrova Anastasia
Published: January 2023

Let

k

be a field of characteristic 0. Let

G

be a reductive group over the ring of Laurent polynomials

R=k[x_1^{\pm 1},\ldots,x_n^{\pm 1}]

. We prove that

G

is isotropic over

R

if and only if it is isotropic over the field of fractions

k(x_1,\ldots,x_n)

of

R

, and if this is the case, then the natural map

H^1_{\acute{e}t}(R,G)\to H^1_{\acute{e}t}(k(x_1,\ldots,x_n),G)

has trivial kernel and

G

is loop reductive. In particular, we settle in positive the conjecture of V. Chernousov, P. Gille, and A. Pianzola that

H^1_{Zar}(R,G)=\ast

for such groups

G

. We also deduce that if

G

is a reductive group over

R

of isotropic rank

\ge 2

, then the natural map of non-stable

K_1

-functors

K_1^G(R)\to K_1^G\bigl( k((x_1))\ldots((x_n)) \bigr)

is injective, and an isomorphism if

G

is moreover semisimple.
A pairing on the cuspidal eigenvariety for $\text{GSp}_{2g}$ and the ramification locus
Authors: Wu Ju-Feng
Published: January 2023

In the present paper, we first construct a pairing on the space of analytic distributions associated with

\text{GSp}_{2g}

. By considering the overconvergent parabolic cohomology groups and following the work of Johansson-Newton, we construct the cuspidal eigenvariety for

\text{GSp}_{2g}

. The pairing on the analytic distributions then induces a pairing on some coherent sheaves of the cuspidal eigenvariety. As an application, we follow the strategy of Bellaïche to study the ramification locus of the cuspidal eigenvariety over the corresponding weight space.
Non-commensurable hyperbolic manifolds with the same trace ring
Authors: Mila Olivier
Published: January 2023

We prove that there are infinitely many pairwise non-commensurable hyperbolic

n

-manifolds that have the same ambient group and trace ring, for any

n \geq 3

. The manifolds can be chosen compact, if

n \geq 4

.
Hearts for commutative Noetherian rings: torsion pairs and derived equivalences
Authors: Pavon Sergio , Vitória Jorge
Published: January 2023

Over a commutative noetherian ring

R

, the prime spectrum controls, via the assignment of support, the structure of both

\mathsf{Mod}(R)

and

\mathsf{D}(R)

. We show that, just like in

\mathsf{Mod}(R)

, the assignment of support classifies hereditary torsion pairs in the heart of any nondegenerate compactly generated

t

-structure of

\mathsf{D}(R)

. Moreover, we investigate whether these

t

-structures induce derived equivalences, obtaining a new source of Grothendieck categories which are derived equivalent to

\mathsf{Mod}(R)

.
Transfer maps in generalized group homology via submanifolds
Authors: Nitsche Martin , Schick Thomas , Zeidler Rudolf
Published: January 2023

Let

N \subset M

be a submanifold embedding of spin manifolds of some codimension

k \geq 1

. A classical result of Gromov and Lawson, refined by Hanke, Pape and Schick, states that

M

does not admit a metric of positive scalar curvature if

k = 2

and the Dirac operator of

N

has non-trivial index, provided that suitable geometric conditions on

N \subset M

are satisfied. In the cases

k=1

and

k=2

, Zeidler and Kubota, respectively, established more systematic results: There exists a transfer

\text{KO}_\ast(\text{C}^{\ast} \pi_1 M)\to \text{KO}_{\ast - k}(\text{C}^\ast \pi_1 N)

which maps the index class of

M

to the index class of

N

. The main goal of this article is to construct analogous transfer maps

E_\ast(\text{B}\pi_1M) \to E_{\ast-k}(\text{B}\pi_1N)

for different generalized homology theories

E

and suitable submanifold embeddings. The design criterion is that it is compatible with the transfer

E_\ast(M) \to E_{\ast-k}(N)

induced by the inclusion

N \subset M

for a chosen orientation on the normal bundle. Under varying restrictions on homotopy groups and the normal bundle, we construct transfers in the following cases in particular: In ordinary homology, it works for all codimensions. This slightly generalizes a result of Engel and simplifies his proof. In complex K-homology, we achieve it for

k \leq 3

. For

k \leq 2

, we have a transfer on the equivariant KO-homology of the classifying space for proper actions.
Local acyclicity in $p$-adic cohomology
Authors: Lazda Christopher
Published: January 2023

We prove an analogue for

p

-adic coefficients of the Deligne-Laumon theorem on local acyclicity for curves. That is, for an overconvergent

F

-isocrystal

E

on a relative curve

f:U\rightarrow S

admitting a good compactification, we show that the cohomology sheaves of

\mathbf{R}f_!E

are overconvergent isocrystals if and only if

E

has constant Swan conductor at infinity.
Projective bundle theorem in MW-motivic cohomology
Authors: Yang Nanjun
Published: January 2023

We present a version of projective bundle theorem in MW-motives (resp. Chow-Witt rings), which says that

\widetilde{CH}^*(\mathbb{P}(E))

is determined by

\widetilde{CH}^*(X), \widetilde{CH}^*(X,det(E)^{\vee}), CH^*(X)

and

Sq^2

for smooth quasi-projective schemes

X

and vector bundles

E

over

X

with

e(E^{\vee})=0\in H^n(X,W(det(E)))

, provided that

_2CH^*(X)=0

.

As an application, we compute the MW-motives of blow-ups with smooth centers. Moreover, we discuss the invariance of Chow-Witt cycles of projective bundles under automorphisms of vector bundles.
Algebraic slice spectral sequences
Authors: Culver Dominic Leon , Kong Hana Jia , Quigley J. D.
Published: January 2023

For certain motivic spectra, we construct a square of spectral sequences relating the effective slice spectral sequence and the motivic Adams spectral sequence. We show the square can be constructed for connective algebraic K-theory, motivic Morava K-theory, and truncated motivic Brown-Peterson spectra. In these cases, we show that the

\mathbb{R}

-motivic effective slice spectral sequence is completely determined by the

\rho

-Bockstein spectral sequence. Using results of Heard, we also obtain applications to the Hill-Hopkins-Ravenel slice spectral sequences for connective Real K-theory, Real Morava K-theory, and truncated Real Brown-Peterson spectra.
Relations between infinitesimal non-commutative cumulants
Authors: Celestino Adrián , Ebrahimi-Fard Kurusch , Perales Daniel
Published: January 2023

Boolean, free and monotone cumulants as well as relations among them, have proven to be important in the study of non-commutative probability theory. Quite notably, Boolean cumulants were successfully used to study free infinite divisibility via the Boolean Bercovici-Pata bijection. On the other hand, in recent years the concept of infinitesimal non-commutative probability has been developed, together with the notion of infinitesimal cumulants which can be useful in the context of combinatorial questions.

In this paper, we show that the known relations among free, Boolean and monotone cumulants still hold in the infinitesimal framework. Our approach is based on the use of algebra of Grassmann numbers. Formulas involving infinitesimal cumulants can be obtained by applying a formal derivation to known formulas.

The relations between the various types of cumulants turn out to be captured via the shuffle algebra approach to moment-cumulant relations in non-commutative probability theory. In this formulation, (free, Boolean and monotone) cumulants are represented as elements of the Lie algebra of infinitesimal characters over a particular combinatorial Hopf algebra. The latter consists of the graded connected double tensor algebra defined over a non-commutative probability space and is neither commutative nor cocommutative. In this note it is shown how the shuffle algebra approach naturally extends to the notion of infinitesimal non-commutative probability space. The basic step consists in replacing the base field as target space of linear Hopf algebra maps by the algebra of Grassmann numbers defined over the base field. We also consider the infinitesimal analog of the Boolean Bercovici-Pata map.
$I_n$-local Johnson-Wilson spectra and their Hopf algebroids
Authors: Baker Andrew
Published: January 2023

We consider a generalization

\mathcal{E}(n)

of the Johnson-Wilson spectrum

E(n)

for which

\mathcal{E}(n)_*

is a local ring with maximal ideal

I_n

. We prove that the spectra

E(n), \mathcal{E}(n)

and

\widehat{E(n)}

are Bousfield equivalent. We also show that the Hopf algebroid

\mathcal{E}(n)_*\mathcal{E}(n)

is a free

\mathcal{E}(n)_*

-module, generalizing a result of Adams and Clarke for

KU_*KU

.
Some homological properties of category $\mathcal{O}$. VI
Authors: Ko Hankyung , Mazorchuk Volodymyr , Mrden Rafael
Published: January 2023

This paper explores various homological regularity phenomena (in the sense of Auslander) in category

\mathcal{O}

and its several variations and generalizations. Additionally, we address the problem of determining projective dimension of twisted and shuffled projective and tilting modules.
Drinfeld's lemma for perfectoid spaces and overconvergence of multivariate $(\varphi, \Gamma)$-modules
Authors: Carter Annie , Kedlaya Kiran S. , Zábrádi Gergely
Published: January 2023

Let

p

be a prime, let

K

be a finite extension of

\mathbb{Q}_p

, and let

n

be a positive integer. We construct equivalences of categories between continuous

p

-adic representations of the

n

-fold product of the absolute Galois group

G_K

and

(\varphi, \Gamma)

-modules over one of several rings of

n

-variable power series. The case

n=1

recovers the original construction of Fontaine and the subsequent refinement by Cherbonnier-Colmez; for general

n

, the case

K = \mathbb{Q}_p

had been previously treated by the third author. To handle general

K

uniformly, we use a form of Drinfeld's lemma on the profinite fundamental groups of products of spaces in characteristic

p

, but for perfectoid spaces instead of schemes. We also construct the multivariate analogue of the Herr complex to compute Galois cohomology; the case

K = \mathbb{Q}_p

had been previously treated by Pal and the third author, and we reduce to this case using a form of Shapiro's lemma.
On the James and Hilton-Milnor splittings, and the metastable EHP sequence
Authors: Devalapurkar Sanath , Haine Peter
Published: January 2023

This note provides modern proofs of some classical results in algebraic topology, such as the James Splitting, the Hilton–Milnor Splitting, and the metastable EHP sequence. We prove fundamental splitting results

\Sigma \Omega \Sigma X \simeq \Sigma X \vee (X\wedge \Sigma\Omega \Sigma X)

and

\Omega(X \vee Y) \simeq \Omega X\times \Omega Y\times \Omega \Sigma(\Omega X \wedge \Omega Y)

in the maximal generality of an

\infty

-category with finite limits and pushouts in which pushouts squares remain pushouts after basechange along an arbitrary morphism (i.e., Mather's Second Cube Lemma holds). For connected objects, these imply the classical James and Hilton–Milnor splittings. Moreover, working in this generality shows that the James and Hilton–Milnor splittings hold in many new contexts, for example in: elementary

\infty

-topoi, profinite spaces, and motivic spaces over arbitrary base schemes. The splitting results in this last context extend Wickelgren and Williams' splitting result for motivic spaces over a perfect field [
K. Wickelgren
and
B. Williams
, Geom. Topol. 23, No. 4, 1691–1777 (2019; Zbl 1428.14032)]. We also give two proofs of the metastable EHP sequence in the setting of

\infty

-topoi: the first is a new, non-computational proof that only utilizes basic connectedness estimates involving the James filtration and the Blakers–Massey Theorem, while the second reduces to the classical computational proof.