bluuebunny/crossref_metadata_2025 huggingface dataset:
Divisibility of the Dirac magnetic monopole as a two-vector bundle over the three-sphere
Authors: Ausoni Christian , Dundas Bjørn Ian , Rognes John
Published: January 2023

We show that when the gerbe

\mu

representing a magnetic monopole is viewed as a virtual 2-vector bundle, then it decomposes, modulo torsion, as two times a virtual 2-vector bundle

\varsigma

. We therefore interpret

\varsigma

as representing half a magnetic monopole, or a semipole.
The global structure of moduli spaces of polarized $p$-divisible groups
Authors: Viehmann Eva
Published: January 2023

We study the global structure of moduli spaces of quasi-isogenies of polarized

p

-divisible groups introduced by Rapoport and Zink. Using the corresponding results for non-polarized

p

-divisible groups from a previous paper, we determine their dimensions and their sets of connected components and of irreducible components.
Chow-Künneth decomposition for some moduli spaces
Authors: Iyer Jaya Nn. , Müller-Stach Stefan
Published: January 2023

In this paper we investigate Murre's conjecture on the Chow–Künneth decomposition for universal families of smooth curves over spaces which dominate the moduli space

\mathcal M_g

, in genus at most 8 and show existence of a Chow–Künneth decomposition. This is done in the setting of equivariant cohomology and equivariant Chow groups to get equivariant Chow–Künneth decompositions.
Projective homogeneous varieties birational to quadrics
Authors: MacDonald Mark L.
Published: January 2023

We will consider an explicit birational map between a quadric and the projective variety

X(J)

of traceless rank one elements in a simple reduced Jordan algebra

J. X(J)

is a homogeneous

G

-variety for the automorphism group

G=\textup{Aut}(J)

. We will show that the birational map is a blow up followed by a blow down. This will allow us to use the blow up formula for motives together with Vishik's work on the motives of quadrics to give a motivic decomposition of

X(J)

.
Rationally connected foliations on surfaces
Authors: Neumann Sebastian
Published: January 2023

In this short note we study foliations on surfaces with rationally connected leaves. Our main result is that on a surface there exists a polarisation such that the Harder-Narasimhan filtration of the tangent bundle with respect to this polarisation yields the maximal rationally connected quotient of the surface.
The Allegretto-Piepenbrink theorem for strongly local Dirichlet forms
Authors: Lenz Daniel , Stollmann Peter , Veselić Ivan
Published: January 2023

The existence of positive weak solutions is related to spectral information on the corresponding partial differential operator.
Compact complex manifolds with numerically effective cotangent bundles
Authors: Kratz Henrik
Published: January 2023

We prove that a projective manifold of dimension

n=2

or 3 and Kodaira dimension 1 has a numerically effective cotangent bundle if and only if the Iitaka fibration is almost smooth, i.e. the only singular fibres are multiples of smooth elliptic curves (

n=2

) resp. multiples of smooth Abelian or hyperelliptic surfaces (

n=3

). In the case of a threefold which is fibred over a rational curve the proof needs an extra assumption concerning the multiplicities of the singular fibres. Furthermore, we prove the following theorem: let

X

be a complex manifold which is hyberbolic with respect to the Carathéodory-Reiffen-pseudometric, then any compact quotient of

X

has a numerically effective cotangent bundle.
The max-plus Martin boundary
Authors: Akian Marianne , Gaubert Stéphane , Walsh Cormac
Published: January 2023

We develop an idempotent version of probabilistic potential theory. The goal is to describe the set of max-plus harmonic functions, which give the stationary solutions of deterministic optimal control problems with additive reward. The analogue of the Martin compactification is seen to be a generalisation of the compactification of metric spaces using (generalised) Busemann functions. We define an analogue of the minimal Martin boundary and show that it can be identified with the set of limits of «almost-geodesics», and also the set of (normalised) harmonic functions that are extremal in the max-plus sense. Our main result is a max-plus analogue of the Martin representation theorem, which represents harmonic functions by measures supported on the minimal Martin boundary. We illustrate it by computing the eigenvectors of a class of Lax-Oleinik semigroups with nondifferentiable Lagrangian: we relate extremal eigenvector to Busemann points of normed spaces.
Spectral analysis of relativistic atoms -- Dirac operators with singular potentials
Authors: Huber Matthias
Published: January 2023

This is the first part of a series of two papers, which investigate spectral properties of Dirac operators with singular potentials. We examine various properties of complex dilated Dirac operators. These operators arise in the investigation of resonances using the method of complex dilations. We generalize the spectral analysis of Weder citeWeder1973 and Šeba citeSeba1988 to operators with Coulomb type potentials, which are not relatively compact perturbations. Moreover, we define positive and negative spectral projections as well as transformation functions between different spectral subspaces and investigate the non-relativistic limit of these operators. We will apply these results in citeHuber2008O in the investigation of resonances in a relativistic Pauli-Fierz model, but they might also be of independent interest.
The energy of heavy atoms according to Brown and Ravenhall: the Scott correction
Authors: Frank Rupert L. , Siedentop Heinz , Warzel Simone
Published: January 2023

We consider relativistic many-particle operators which – according to Brown and Ravenhall – describe the electronic states of heavy atoms. Their ground state energy is investigated in the limit of large nuclear charge and velocity of light. We show that the leading quasi-classical behavior given by the Thomas–Fermi theory is raised by a subleading correction, the Scott correction. Our result is valid for the maximal range of coupling constants, including the critical one. As a technical tool, a Sobolev–Gagliardo–Nirenberg-type inequality is established for the critical atomic Brown–Ravenhall operator. Moreover, we prove sharp upper and lower bounds on the eigenvalues of the hydrogenic Brown–Ravenhall operator up to and including the critical coupling constant.
Geometric description of the connecting homomorphism for Witt groups
Authors: Balmer Paul , Calmès Baptiste
Published: January 2023

We give a geometric setup in which the connecting homomorphism in the localization long exact sequence for Witt groups decomposes as the pull-back to the exceptional fiber of a suitable blow-up followed by a push-forward.
Motivic Landweber exactness
Authors: Naumann Niko , Spitzweck Markus , Østvær Paul Arne
Published: January 2023

We prove a motivic Landweber exact functor theorem. The main result shows the assignment given by a Landweber-type formula involving the

\mathsf{MGL}

-homology of a motivic spectrum defines a homology theory on the motivic stable homotopy category which is representable by a Tate spectrum. Using a universal coefficient spectral sequence we deduce formulas for operations of certain motivic Landweber exact spectra including homotopy algebraic

K

-theory. Finally we employ a Chern character between motivic spectra in order to compute rational algebraic cobordism groups over fields in terms of rational motivic cohomology groups and the Lazard ring.
Affine simplices in Oka manifolds
Authors: Lárusson Finnur
Published: January 2023

We show that the homotopy type of a complex manifold

X

satisfying the Oka property is captured by holomorphic maps from the affine spaces

\mathbb C^n, n\geq 0

, into

X

. Among such

X

are all complex Lie groups and their homogeneous spaces. We present generalisations of this result, one of which states that the homotopy type of the space of continuous maps from any smooth manifold to

X

is given by a simplicial set whose simplices are holomorphic maps into

X

.
Twisted cohomology of the Hilbert schemes of points on surfaces
Authors: Nieper-Wißkirchen Marc A.
Published: January 2023

We calculate the cohomology spaces of the Hilbert schemes of points on surfaces with values in local systems. For that purpose, we generalise I. Grojnoswki's and H. Nakajima's description of the ordinary cohomology in terms of a Fock space representation to the twisted case. We make further non-trivial generalisations of M. Lehn's work on the action of the Virasoro algebra to the twisted and the non-projective case. Building on work by M. Lehn and Ch. Sorger, we then give an explicit description of the cup-product in the twisted case whenever the surface has a numerically trivial canonical divisor. We formulate our results in a way that they apply to the projective and non-projective case in equal measure. As an application of our methods, we give explicit models for the cohomology rings of the generalised Kummer varieties and of a series of certain even dimensional Calabi–Yau manifolds.
The Sato-Tate conjecture for modular forms of weight 3
Authors: Gee Toby
Published: January 2023

We prove a natural analogue of the Sato-Tate conjecture for modular forms of weight 2 or 3 whose associated automorphic representations are a twist of the Steinberg representation at some finite place.
Subproduct systems
Authors: Shalit Orr , Solel Baruch
Published: January 2023

The notion of a subproduct system, a generalization of that of a product system, is introduced. We show that there is an essentially 1 to 1 correspondence between

cp

-semigroups and pairs

(X,T)

where

X

is a subproduct system and

T

is an injective subproduct system representation. A similar statement holds for subproduct systems and units of subproduct systems. This correspondence is used as a framework for developing a dilation theory for

cp

-semigroups. Results we obtain: (i) a *-automorphic dilation to semigroups of *-endomorphisms over quite general semigroups; (ii) necessary and sufficient conditions for a semigroup of CP maps to have a *-endomorphic dilation; (iii) an analogue of Parrot's example of three contractions with no isometric dilation, that is, an example of three commuting, contractive normal CP maps on

B(H)

that admit no *-endomorphic dilation (thereby solving an open problem raised by Bhat in 1998). Special attention is given to subproduct systems over the semigroup

{N}

, which are used as a framework for studying tuples of operators satisfying homogeneous polynomial relations, and the operator algebras they generate. As applications we obtain a noncommutative (projective) Nullstellensatz, a model for tuples of operators subject to homogeneous polynomial relations, a complete description of all representations of Matsumoto's subshift C^*-algebra when the subshift is of finite type, and a classification of certain operator algebras – including an interesting non-selfadjoint generalization of the noncommutative tori.
Standard relations of multiple polylogarithm values at roots of unity
Authors: Zhao Jianqiang
Published: January 2023

Let

N

be a positive integer. In this paper we shall study the special values of multiple polylogarithms at

N

th roots of unity, called multiple polylogarithm values (MPVs) of level

N

. Our primary goal in this paper is to investigate the relations among the MPVs of the same weight and level by using the regularized double shuffle relations, regularized distribution relations, lifted versions of such relations from lower weights, and weight one relations which are produced by relations of weight one MPVs. We call relations from the above four families
standard
. Let

d(w,N)

be the dimension of the

\mathbb Q

-vector space generated by all MPVs of weight

w

and level

N

. Recently Deligne and Goncharov were able to obtain some lower bound of

d(w,N)

using the motivic mechanism. We call a level

N

standard if

N=1,2,3

or

N=p^n

for prime

p\ge 5

. Our computation suggests the following dichotomy: If

N

is standard then the standard relations should produce all the linear relations and if further

N>3

then the bound of

d(w,N)

by Deligne and Goncharov can be improved; otherwise there should be non-standard relations among MPVs for all sufficiently large weights (depending only on

N

) and the bound by Deligne and Goncharov may be sharp. We write down some of the non-standard relations explicitly with good numerical verification. In two instances (

N=4, w=3,4

) we can rigorously prove these relations by using the octahedral symmetry of

{0,\infty,\pm1,\pm\sqrt{-1}}

. Throughout the paper we provide many conjectures which are strongly supported by computational evidence.
Singular Bott-Chern classes and the arithmetic Grothendieck Riemann Roch theorem for closed immersions
Authors: Burgos Gil José I. , Litcanu Razvan
Published: January 2023

We study the singular Bott-Chern classes introduced by Bismut, Gillet and Soulé. Singular Bott-Chern classes are the main ingredient to define direct images for closed immersions in arithmetic

K

-theory. In this paper we give an axiomatic definition of a theory of singular Bott-Chern classes, study their properties, and classify all possible theories of this kind. We identify the theory defined by Bismut, Gillet and Soulé as the only one that satisfies the additional condition of being homogeneous. We include a proof of the arithmetic Grothendieck-Riemann-Roch theorem for closed immersions that generalizes a result of Bismut, Gillet and Soulé and was already proved by Zha. This result can be combined with the arithmetic Grothendieck-Riemann-Roch theorem for submersions to extend this theorem to arbitrary projective morphisms. As a byproduct of this study we obtain two results of independent interest. First, we prove a Poincaré lemma for the complex of currents with fixed wave front set, and second we prove that certain direct images of Bott-Chern classes are closed.
On higher order estimates in quantum electrodynamics
Authors: Matte Oliver
Published: January 2023

We propose a new method to derive certain higher order estimates in quantum electrodynamics. Our method is particularly convenient in the application to the non-local semi-relativistic models of quantum electrodynamics as it avoids the use of iterated commutator expansions. We re-derive higher order estimates obtained earlier by Fröhlich, Griesemer, and Schlein and prove new estimates for a non-local molecular no-pair operator.
Laplace transform representations and Paley-Wiener theorems for functions on vertical strips
Authors: Harper Zen
Published: January 2023

We consider the problem of representing an analytic function on a vertical strip by a bilateral Laplace transform. We give a Paley–Wiener theorem for weighted Bergman spaces on the existence of such representations, with applications. We generalise a result of Batty and Blake, on abscissae of convergence and boundedness of analytic functions on halfplanes, and also consider harmonic functions. We consider analytic continuations of Laplace transforms, and uniqueness questions: if an analytic function is the Laplace transform of functions

f_1, f_2

on two disjoint vertical strips, and extends analytically between the strips, when is

f_1=f_2

? We show that this is related to the uniqueness of the Cauchy problem for the heat equation with complex space variable, and give some applications, including a new proof of a Maximum Principle for harmonic functions.
Local classes and pairwise mutually permutable products of finite groups.
Authors: Ballester-Bolinches A. , Beidleman J.C. , Heineken H. , Pedraza-Aguilera M.C.
Published: January 2023

The main aim of the paper is to present some results about products of pairwise mutually permutable subgroups and local classes.
The index of centralizers of elements of reductive Lie algebras
Authors: Charbonnel Jean-Yves , Moreau Anne
Published: January 2023

For a finite dimensional complex Lie algebra, its index is the minimal dimension of stabilizers for the coadjoint action. A famous conjecture due to A.G. Elashvili says that the index of the centralizer of an element of a reductive Lie algebra is equal to the rank. That conjecture caught attention of several Lie theorists for years. It reduces to the case of nilpotent elements. In citePa1 and citePa2, D.I. Panyushev proved the conjecture for some classes of nilpotent elements (e.g. regular, subregular and spherical nilpotent elements). Then the conjecture has been proven for the classical Lie algebras in citeY1 and checked with a computer programme for the exceptional ones citeDe. In this paper we give an almost general proof of that conjecture.
The cohomology rings of moduli stacks of principal bundles over curves
Authors: Heinloth Jochen , Schmitt Alexander H.W.
Published: January 2023

We prove that the cohomology of the moduli stack of

G

-bundles on a smooth projective curve is freely generated by the Atiyah–Bott classes in arbitrary characteristic. The main technical tool needed is the construction of coarse moduli spaces for bundles with parabolic structure in arbitrary characteristic. Using these spaces we show that the cohomology of the moduli stack is pure and satisfies base-change for curves defined over a discrete valuation ring. Thereby we get an algebraic proof of the theorem of Atiyah and Bott and conversely this can be used to give a geometric proof of the fact that the Tamagawa number of a Chevalley group is the number of connected components of the moduli stack of principal bundles.
Frames and finite group schemes over complete regular local rings
Authors: Lau Eike
Published: January 2023

Let

p

be an odd prime. We show that the classification of

p

-divisible groups by Breuil windows and the classification of commutative finite flat group schemes of

p

-power order by Breuil modules hold over every complete regular local ring with perfect residue field of characteristic

p

. We set up a formalism of frames and windows with an abstract deformation theory that applies to Breuil windows.
Purity results for $p$-divisible groups and Abelian schemes over regular bases of mixed characteristic
Authors: Vasiu Adrian , Zink Thomas
Published: January 2023

Let

p

be a prime. Let

(R,\mathfrak m)

be a regular local ring of mixed characteristic

(0,p)

and absolute index of ramification

e

. We provide general criteria of when each abelian scheme over

\operatorname{Spec} R\setminus{\mathfrak m}

extends to an abelian scheme over

\operatorname{Spec} R

. We show that such extensions always exist if

e \le p-1

, exist in most cases if

p \le e \le 2p-3

, and do not exist in general if

e\ge 2p-2

. The case

e \le p-1

implies the uniqueness of integral canonical models of Shimura varieties over a discrete valuation ring

O

of mixed characteristic

(0,p)

and index of ramification at most

p-1

. This leads to large classes of examples of Néron models over

O

. If

p>2

and index

p-1

, the examples are new.
Hankel operators and the Dixmier trace on strictly pseudoconvex domains
Authors: Englis Miroslav
Published: January 2023

Generalizing earlier results for the disc and the ball, we give a formula for the Dixmier trace of the product of

2n

Hankel operators on Bergman spaces of strictly pseudoconvex domains in

\bold C^n

. The answer turns out to involve the dual Levi form evaluated on boundary derivatives of the symbols. Our main tool is the theory of generalized Toeplitz operators due to Boutet de Monvel and Guillemin.
Galois representations attached to Hilbert–Siegel modular forms
Authors: Sorensen Claus M.
Published: January 2023

This article is a spinoff of the book of Harris and Taylor [HT], in which they prove the local Langlands conjecture for

\operatorname{GL}(n)

, and its companion paper by Taylor and Yoshida [TY] on local-global compatibility. We record some consequences in the case of genus two Hilbert–Siegel modular forms. In other words, we are concerned with cusp forms

\pi

on

\operatorname{GSp}(4)

over a totally real field, such that

\pi_{\infty}

is regular algebraic (that is,

\pi

is cohomological). When

\pi

is globally generic (that is, has a non-vanishing Fourier coefficient), and

\pi

has a Steinberg component at some finite place, we associate a Galois representation compatible with the local Langlands correspondence for

\operatorname{GSp}(4)

defined by Gan and Takeda in a recent preprint [GT]. Over

\mathbb Q

, for

\pi

as above, this leads to a new realization of the Galois representations studied previously by Laumon, Taylor and Weissauer. We are hopeful that our approach should apply more generally, once the functorial lift to

\operatorname{GL}(4)

is understood, and once the so-called book project is completed. An application of the above compatibility is the following special case of a conjecture stated in [SU]: If

\pi

has nonzero vectors fixed by a non-special maximal compact subgroup at

v

, the corresponding monodromy operator at

v

has rank at most one.
Arithmetic of a fake projective plane and related elliptic surfaces
Authors: Džambić Amir
Published: January 2023

The purpose of the present paper is to explain the fake projective plane constructed by J. H. Keum from the point of view of arithmetic ball quotients. Beside the ball quotient associated with the fake projective plane, we also analize two further naturally related ball quotients whose minimal desingularizations lead to two elliptic surfaces, one already considered by J. H. Keum as well as the one constructed by M. N. Ishida in terms of p-adic uniformization.
An inverse $K$-theory functor
Authors: Mandell Michael A.
Published: January 2023

Thomason showed that the

K

-theory of symmetric monoidal categories models all connective spectra. This paper describes a new construction of a permutative category from a

\Gamma

-space, which is then used to re-prove Thomason's theorem and a non-completed variant.
On reductions of families of crystalline Galois representations
Authors: Dousmanis Gerasimos
Published: January 2023

Let

K_f

be the finite unramified extension of

{Q}_p

of degree

f

and

E

any finite large enough coefficient field containing

K_f.

We construct analytic families of étale

(\varphi ,\Gamma )

-modules which give rise to families of crystalline

E

-representations of the absolute Galois group

G_{K_f}

of

K_f.

For any irreducible effective two-dimensional crystalline

E

-representation of

G_{K_f}

with labeled Hodge-Tate weights

{0,-k_i}_{\tau _i}

induced from a crystalline character of

G_{K_{2f}},

we construct an infinite family of crystalline

E

-representations of

G_{K_f}

of the same Hodge-Tate type which contains it. As an application, we compute the semisimplified mod

p

reductions of the members of each such family.
Almost proper GIT-stacks and discriminant avoidance
Authors: Starr Jason , De Jong Johan
Published: January 2023

We prove that the classifying stack of an reductive group scheme over a field is very close to being proper. Using this we prove a result about isotrivial families of varieties. Fix a polarized variety with reductive automorphism group. To prove that every isotrivial family with this fibre has a rational section it suffices to prove this when the base is projective, i.e., the discriminant of the family is empty.
Good reduction of affinoids on the Lubin-Tate tower
Authors: Weinstein Jared
Published: January 2023

We analyze the geometry of the tower of Lubin-Tate deformation spaces, which parametrize deformations of a one-dimensional formal module of height

h

together with level structure. According to the conjecture of Deligne-Carayol, these spaces realize the local Langlands correspondence in their

\ell

-adic cohomology. This conjecture is now a theorem, but currently there is no purely local proof. Working in the equal characteristic case, we find a family of affinoids in the Lubin-Tate tower with good reduction equal to a rather curious nonsingular hypersurface, whose equation we present explicitly. Granting a conjecture on the

L

-functions of this hypersurface, we find a link between the conjecture of Deligne-Carayol and the theory of Bushnell-Kutzko types, at least for certain class of wildly ramified supercuspidal representations of small conductor.
Emerton's Jacquet functors for non-Borel parabolic subgroups
Authors: Hill Richard , Loeffler David
Published: January 2023

This paper studies Emerton's Jacquet module functor for locally analytic representations of

p

-adic reductive groups, introduced in citeemerton-jacquet. When

P

is a parabolic subgroup whose Levi factor

M

is not commutative, we show that passing to an isotypical subspace for the derived subgroup of

M

gives rise to essentially admissible locally analytic representations of the torus

Z(M)

, which have a natural interpretation in terms of rigid geometry. We use this to extend the construction in of eigenvarieties in citeemerton-interpolation by constructing eigenvarieties interpolating automorphic representations whose local components at

p

are not necessarily principal series.
Multigraded factorial rings and Fano varieties with torus action
Authors: Hausen Jürgen , Herppich Elaine , Süss Hendrik
Published: January 2023

In a first result, we describe all finitely generated factorial algebras over an algebraically closed field of characteristic zero that come with an effective multigrading of complexity one by means of generators and relations. This enables us to construct systematically varieties with free divisor class group and a complexity one torus action via their Cox rings. For the Fano varieties of this type that have a free divisor class group of rank one, we provide explicit bounds for the number of possible deformation types depending on the dimension and the index of the Picard group in the divisor class group. As a consequence, one can produce classification lists for fixed dimension and Picard index. We carry this out expemplarily in the following cases. There are 15 non-toric surfaces with Picard index at most six. Moreover, there are 116 non-toric threefolds with Picard index at most two; nine of them are locally factorial, i.e. of Picard index one, and among these one is smooth, six have canonical singularities and two have non-canonical singularities. Finally, there are 67 non-toric locally factorial fourfolds and two one-dimensional families of non-toric locally factorial fourfolds. In all cases, we list the Cox rings explicitly.
On the structure of covers of sofic shifts
Authors: Johansen Rune
Published: January 2023

A canonical cover generalizing the left Fischer cover to arbitrary sofic shifts is introduced and used to prove that the left Krieger cover and the past set cover of a sofic shift can be divided into natural layers. These results are used to find the range of a flow-invariant and to investigate the ideal structure of the universal

C^*

-algebra associated to a sofic shift space.
Supplement on curved flats in the space of point pairs and isothermic surfaces: A quaternionic calculus
Authors: Hertrich-Jeromin Udo
Published: January 2023

A quaternionic calculus for surface pairs in the conformal 4-sphere is elaborated. It introduces a rich algebraic structure and allows the use of global frames while, at the same time, incorporates the classical “geometric” model of Möbius geometry providing geometric clarity. This way, it provides the foundation for the development of new techniques in Möbius differential geometry.
An infinite level atom coupled to a heat bath
Authors: Koenenberg M.
Published: January 2023

We consider a

W^*

-dynamical system

(\mathfrak M_\beta,\tau)

, which models finitely many particles coupled to an infinitely extended heat bath. The energy of the particles can be described by an unbounded operator, which has infinitely many energy levels. We show existence of the dynamics

\tau

and existence of a

(\beta,\tau)

-KMS state under very explicit conditions on the strength of the interaction and on the inverse temperature

\beta

.
Divisorial cohomology vanishing on toric varieties
Authors: Perling Markus
Published: January 2023

This work discusses combinatorial and arithmetic aspects of cohomology vanishing for divisorial sheaves on toric varieties. We obtain a refined variant of the Kawamata-Viehweg theorem which is slightly stronger. Moreover, we prove a new vanishing theorem related to divisors whose inverse is nef and has small Iitaka dimension. Finally, we give a new criterion for divisorial sheaves for being maximal Cohen-Macaulay.
Algebraic zip data
Authors: Pink Richard , Wedhorn Torsten , Ziegler Paul
Published: January 2023

An algebraic zip datum is a tuple

\mathcal Z = (G,P,Q,\varphi)

consisting of a reductive group

G

together with parabolic subgroups

P

and

Q

and an isogeny

\varphi\colon P/R_uP\to Q/R_uQ

. We study the action of the group

E_{\mathcal Z} := \{ (p,q)\in P{\times}Q | \varphi(\pi_{P}(p)) =\pi_Q(q)\}

on

G

given by

((p,q),g)\mapsto pgq^{-1}

. We define certain smooth

E_{\mathcal Z}

-invariant subvarieties of

G

, show that they define a stratification of

G

. We determine their dimensions and their closures and give a description of the stabilizers of the

E_\mathcal Z

-action on

G

. We also generalize all results to non-connected groups. We show that for special choices of

\mathcal Z

the algebraic quotient stack

[E_{\mathcal Z} \ G]

is isomorphic to

[G \Z]

or to

[G \Z']

, where

Z

is a

G

-variety studied by Lusztig and He in the theory of character sheaves on spherical compactifications of

G

and where

Z'

has been defined by Moonen and the second author in their classification of

F

-zips. In these cases the

E_{\mathcal Z}

-invariant subvarieties correspond to the so-called “

G

-stable pieces” of

Z

defined by Lusztig (resp. the

G

-orbits of

Z'

).
Euler characteristics of categories and homotopy colimits
Authors: Fiore Thomas M. , Lück Wolfgang , Sauer Roman
Published: January 2023

In a previous article, we introduced notions of finiteness obstruction, Euler characteristic, and

L^2

-Euler characteristic for wide classes of categories. In this sequel, we prove the compatibility of those notions with homotopy colimits of

\mathcal I

-indexed categories where

\mathcal I

is any small category admitting a finite

\mathcal I

-

CW

-model for its

\mathcal I

-classifying space. Special cases of our Homotopy Colimit Formula include formulas for products, homotopy pushouts, homotopy orbits, and transport groupoids. We also apply our formulas to Haefliger complexes of groups, which extend Bass–Serre graphs of groups to higher dimensions. In particular, we obtain necessary conditions for developability of a finite complex of groups from an action of a finite group on a finite category without loops.
Stein surfaces associated to intermediate Kato surfaces
Authors: Battisti Laurent
Published: January 2023

Soient

S

une surface de Kato intermédiaire,

D

le diviseur formé des courbes rationnelles de

S, \widetilde{S}

le revêtement universel de

S

et

\widetilde{D}

la préimage de

D

dans

\widetilde{S}

. On donne deux résultats concernant la surface

\widetilde{S}\setminus \widetilde{D}

, à savoir qu'elle est de Stein (ce qui était connu dans le cas où

S

est une surface d'Enoki ou d'Inoue-Hirzebruch) et on donne une condition nécessaire et suffisante pour que son fibré tangent holomorphe soit holomorphiquement trivialisable.
Moduli of framed sheaves on projective surfaces
Authors: Bruzzo Ugo , Markushevish Dimitri
Published: January 2023

We show that there exists a fine moduli space for torsion-free sheaves on a projective surface which have a “good framing” on a big and nef divisor. This moduli space is a quasi-projective scheme. This is accomplished by showing that such framed sheaves may be considered as stable pairs in the sense of Huybrechts and Lehn. We characterize the obstruction to the smoothness of the moduli space and discuss some examples on rational surfaces.
The additivity theorem in algebraic $K$-theory
Authors: Grayson Daniel R.
Published: January 2023

The additivity theorem in algebraic

K

-theory, due to Quillen and Waldhausen, is a basic tool. In this paper we present a new proof, which proceeds by constructing an explicit homotopy combinatorially.
Witt groups of complex cellular varieties
Authors: Zibrowius Marcus
Published: January 2023

We show that the Grothendieck-Witt and Witt groups of smooth complex cellular varieties can be identified with their topological KO-groups. As an application, we deduce the values of the Witt groups of all irreducible hermitian symmetric spaces, including smooth complex quadrics, spinor varieties and symplectic Grassmannians.
Presentation of an Iwasawa algebra: the case of $\Gamma_1{SL}(2,\Bbb Z_p)$
Authors: Clozel Laurent
Published: January 2023

We give an explicit presentation of the

p

-adic Iwasawa algebra of the subgroup of level one of

SL(2, {Z}_{p})

for

p \neq 2.
On the existence of stationary solutions for some non-Fredholm integro-differential equations
Authors: Vougalter Vitali , Volpert Vitaly
Published: January 2023

We show the existence of stationary solutions for some reaction-diffusion type equations in the appropriate

H^2

spaces using the fixed point technique when the elliptic problem contains second order differential operators with and without Fredholm property.
Fundamental group of Schurian categories and the Hurewicz isomorphism
Authors: Cibils Claude , Redondo María Julia , Solotar Andrea
Published: January 2023

Let

k

be a field. We attach a CW-complex to any Schurian

k

-category and we prove that the fundamental group of this CW-complex is isomorphic to the intrinsic fundamental group of the

k

-category. This extends previous results by J.C. Bustamante in citebu1. We also prove that the Hurewicz morphism from the vector space of abelian characters of the fundamental group to the first Hochschild-Mitchell cohomology vector space of the category is an isomorphism.
Characterizing weak-operator continuous linear functionals on $B(H)$ constructively
Authors: Bridges Douglas S.
Published: January 2023

Let

B(H)

be the space of bounded operators on a not-necessarily-separable Hilbert space

H

. Working within Bishop-style constructive analysis, we prove that certain weak-operator continuous linear functionals on

B(H)

are finite sums of functionals of the form

T\leadsto \langle Tx,y\rangle

. We also prove that the identification of weak- and strong-operator continuous linear functionals on

B(H)

cannot be established constructively.
A simple criterion for extending natural transformations to higher $K$-theory
Authors: Tabuada Gonçalo
Published: January 2023

In this article we introduce a very simple an widely applicable criterion for extending natural transformations to higher

K

-theory. More precisely, we prove that every natural transformation defined on the Grothendieck group and with values in an additive theory admits a unique extension to higher

K

-theory. As an application, the higher trace maps and the higher Chern characters originally constructed by Dennis and Karoubi, respectively, can be obtained in an elegant, unified, and conceptual way from our general results.
Ordinarity of configuration spaces and of wonderful compactifications
Authors: Joshi Kirti
Published: January 2023

We prove the following: (1) if

X

is ordinary, the Fulton-MacPherson configuration space

X[n]

is ordinary for all

n

; (2) the moduli of stable

n

-pointed curves of genus zero is ordinary. (3) More generally we show that a wonderful compactification

X_\mathcal G

is ordinary if and only if

(X,\mathcal G)

is an ordinary building set. This implies the ordinarity of many other well-known configuration spaces (under suitable assumptions).
Stability of $C^*$-algebras is not a stable property
Authors: Rørdam Mikael
Published: January 2023

We show that there exists a

C^*

-algebra

B

such that

M_2(B)

is stable, but

B

is not stable. Hence stability of

C^*

-algebras is not a stable property. More generally, we find for each integer

n \ge 2

a

C^*

-algebra

B

so that

M_n(B)

is stable and

M_k(B)

is not stable when

1 \le k < n

. The

C^*

-algebras we exhibit have the additional properties that they are simple, nuclear and of stable rank one.
Theta series and function field analogue of Gross formula
Authors: Wei Fu-Tsun , Yu Jing
Published: January 2023

Let

k = F_q(t)

, with

q

odd. In this article we introduce «definite» (with respect to the infinite place of

k

) Shimura curves over

k

, and establish Hecke module isomorphisms between their Picard groups and the spaces of Drinfeld type «new» forms of corresponding level. An important application is a function field analogue of Gross formula for the central critical values of Rankin type

L

-series coming from automorphic cusp forms of Drinfeld type.
Extending characters from Hall subgroups.
Authors: Malle Gunter , Navarro Gabriel
Published: January 2023

Suppose that

G

is a finite

\pi

-separable group. A classical result asserts that all irreducible characters of a Hall

\pi

-subgroup

H

of

G

extend to

G

if and only if

H

has a normal complement in

G

. Now, we fix a prime

p

and analyze when only the

p'

-degree irreducible characters of

H

extend to

G

.
Jumps and monodromy of abelian varieties
Authors: Halle Lars Halvard , Nicaise Johannes
Published: January 2023

We prove a strong form of the motivic monodromy conjecture for abelian varieties, by showing that the order of the unique pole of the motivic zeta function is equal to the maximal rank of a Jordan block of the corresponding monodromy eigenvalue. Moreover, we give a Hodge-theoretic interpretation of the fundamental invariants appearing in the proof.
On families of weakly admissible filtered phi-modules and the adjoint quotient of ${GL}_d$
Authors: Hellmann Eugen
Published: January 2023

We study the relation of the notion of weak admissibility in families of filtered

\phi

-modules, as considered in [He], with the adjoint quotient. We show that the weakly admissible subset is an open subvariety in the fibers over the adjoint quotient. Further we determine the image of the weakly admissible set in the adjoint quotient generalizing earlier work of Breuil and Schneider.
Degenerate cohomological Hall algebra and quantized Donaldson-Thomas invariants for $m$-loop quivers.
Authors: Reineke Markus
Published: January 2023

We derive a combinatorial formula for quantized Donaldson-Thomas invariants of the

m

-loop quiver. Our main tools are the combinatorics of noncommutative Hilbert schemes and a degenerate version of the Cohomological Hall algebra of this quiver.
Equivariant cobordism of schemes
Authors: Krishna Amalendu
Published: January 2023

Let

k

be a field of characteristic zero. For a linear algebraic group

G

over

k

acting on a scheme

X

, we define the equivariant algebraic cobordism of

X

and establish its basic properties. We explicitly describe the relation of equivariant cobordism with equivariant Chow groups,

K

-groups and complex cobordism. We show that the rational equivariant cobordism of a

G

-scheme can be expressed as the Weyl group invariants of the equivariant cobordism for the action of a maximal torus of

G

. As applications, we show that the rational algebraic cobordism of the classifying space of a complex linear algebraic group is isomorphic to its complex cobordism.
On the algebraic K-theory of some homogeneous varieties
Authors: Ananyevskiy Alexey
Published: January 2023

The

K

-theory of inner twisted forms of homogeneous varieties

G/H

with connected reductive algebraic groups

H\subset G

of the same rank is computed. We provide an explicit isomorphism with the

K

-theory of certain central simple algebras associated to the considered variety, as a consequence one has that

K_0(G/H)

is a free abelian group of rank

[W(G):W(H)]

. The result is used for the computation of the

K

-theory of some affine homogeneous varieties including an octonionic projective plane and quaternionic projective spaces.
Cohomology of the second Voronoi compactification of $\mathcal A_4$
Authors: Hulek Klaus , Tommasi Orsola
Published: January 2023

In this paper we compute the cohomology groups of the second Voronoi and the perfect cone compactification

\mathcal A^{\mathrm{Vor}}_4

and

\mathcal A^{\mathrm{perf}}_4

respectively, of the moduli space of abelian fourfolds in degree

\leq 9

. The main tool is the investigation of the strata of

\mathcal A^{\mathrm{Vor}}_4

corresponding to semi-abelic varieties with constant torus rank.
On a theorem of Lehrer and Zhang
Authors: Hu Jun , Xiao Zhankui
Published: January 2023

Let

K

be an arbitrary field of characteristic not equal to 2. Let

m, n\in\mathbb N

and

V

be an

m

dimensional orthogonal space over

K

. There is a right action of the Brauer algebra

{\mathfrak B}_n(m)

on the

n

-tensor space

V^{\otimes n}

which centralizes the left action of the orthogonal group

O(V)

. Recently G.I. Lehrer and R.B. Zhang defined certain quasi-idempotents

E_i

in

{\mathfrak B}_n(m)

(see (1.1)) and proved that the annihilator of

V^{\otimes n}

in

{\mathfrak B}_n(m)

is always equal to the two-sided ideal generated by

E_{[(m+1)/2]}

if

\mathrm{char} K=0

or

\mathrm{char} K>2(m+1)

. In this paper we extend this theorem to arbitrary field

K

with

\mathrm{char} K\neq 2

as conjectured by Lehrer and Zhang. As a byproduct, we discover a combinatorial identity which relates to the dimensions of Specht modules over the symmetric groups of different sizes and a new integral basis for the annihilator of

V^{\otimes m+1}

in

{\mathfrak B}_{m+1}(m)

.
On the Weil-étale topos of regular arithmetic schemes
Authors: Flach Matthias , Morin Baptiste
Published: January 2023

We define and study a Weil-étale topos for any regular, proper scheme

\mathcal X

over

\mathrm{Spec}(\mathbb Z)

which has some of the properties suggested by Lichtenbaum for such a topos. In particular, the cohomology with

\tilde{\mathbb R}

-coefficients has the expected relation to

\zeta(\mathcal X,s)

at

s=0

if the Hasse–Weil L-functions

L(h^i(\mathcal X_{\mathbb Q}),s)

have the expected meromorphic continuation and functional equation. If

\mathcal X

has characteristic

p

the cohomology with

\mathbb Z

-coefficients also has the expected relation to

\zeta(\mathcal X,s)

and our cohomology groups recover those previously studied by Lichtenbaum and Geisser.
Simple models of quasihomogeneous projective 3-folds
Authors: Kebekus Stefan
Published: January 2023

Let

X

be a projective complex 3-fold, quasihomogeneous with respect to an action of a linear algebraic group. We show that

X

is a compactification of

SL_2/\Gamma, \Gamma

a finite subgroup, or that

X

can be equivariantly transformed into

\mathbb P_3

, the quadric

\mathbb Q_3

, or into certain quasihomogeneous bundles with very simple structure.
Cyclic cohomology of Lie algebras
Authors: Rangipour Bahram , Sütlü Serkan
Published: January 2023

We define and completely determine the category of Yetter-Drinfeld modules over Lie algebras. We prove a one to one correspondence between Yetter-Drinfeld modules over a Lie algebra and those over the universal enveloping algebra of the Lie algebra. We associate a mixed complex to a Lie algebra and a stable-Yetter-Drinfeld module over it. We show that the (truncated) Weil algebra, the Weil algebra with generalized coefficients defined by Alekseev-Meinrenken, and the perturbed Koszul complex introduced by Kumar-Vergne are examples of such a mixed complex.
Mixed Hodge complexes and $L^2$-cohomology for local systems on ball quotients
Authors: Müller-Stach Stefan , Ye Xuanming , Zuo Kang
Published: January 2023

We study the

L^2

-cohomology of certain local systems on non-compact arithmetic ball quotients

X=\Gamma\setminus \mathbb B_n

. In the case of a ball quotient surface

X

we show that vanishing theorems for

L^2

-cohomology are intimately related to vanishing theorems of the type

H^0(\overline{X}, S^n \Omega^1_{\overline{X}}(\log D) \otimes{\mathcal O}_{\overline{X}}(-D) \otimes (K_{\overline{X}}+D)^{-m/3})=0

for

m \ge n \ge 1

on the toroidal compactification

(\overline{X},D)

. We also give generalizations to higher dimensional ball quotients and study the mixed Hodge structure on the sheaf cohomology of a local system in general with the

L^2

-cohomology contributing to the lowest weight part.
On the structure of Selmer groups of lambda-adic deformations over $p$-adic Lie extensions
Authors: Shekhar Sudhanshu , Sujatha R.
Published: January 2023

In this paper, we consider the

\Lambda

-adic deformations of Galois representations associated to elliptic curves. We prove that the Pontryagin dual of the Selmer group of a

\Lambda

-adic deformation over certain

p

-adic Lie extensions of a number field, that are not necessarily commutative, has no non-zero pseudo-null submodule. We also study the structure of various arithmetic Iwasawa modules associated to such deformations.
An alternative proof of Scheiderer's theorem on the Hasse principle for principal homogeneous spaces
Authors: Chernousov Vladimir
Published: January 2023

We give an alternative proof of the Hasse principle for principal homogeneous spaces defined over fields of virtual cohomological dimension at most one which is based on a special decomposition of elements in Chevalley groups.
The topological Singer construction
Authors: Lunøe-Nielsen Sverre , Rognes John
Published: January 2023

We study the continuous (co-)homology of towers of spectra, with emphasis on a tower with homotopy inverse limit the Tate construction

X^{tG}

on a

G

-spectrum

X

. When

G=C_p

is cyclic of prime order and

X=B^{\wedge p}

is the

p

-th smash power of a bounded below spectrum

B

with

H_*(B; \mathbb F_p)

of finite type, we prove that

(B^{\wedge p})^{tC_p}

is a topological model for the Singer construction

R_+(H^*(B; \mathbb F_p))

on

H^*(B; \mathbb F_p)

. There is a stable map

\epsilon_B : B\to (B^{\wedge p})^{tC_p}

inducing the

\operatorname{Ext}_{\mathcal A}

-equivalence

\epsilon: R_+(H^*(B; \mathbb F_p))\to H^*(B; \mathbb F_p)

. Hence

\epsilon_B

and the canonical map

\Gamma : (B^{\wedge p})^{C_p}\to (B^{\wedge p})^{hC_p}

are

p

-adic equivalences.
The $\Lambda$-adic Shimura-Shintani-Waldspurger correspondence
Authors: Longo Matteo
Published: January 2023

We generalize the

\Lambda

-adic Shintani lifting for

\operatorname{GL}_2(\mathbb Q)

to indefinite quaternion algebras over

\mathbb Q

.
On a positive equicharacteristic variant of the $p$-curvature conjecture
Authors: Esnault Hélène , Langer Adrian
Published: January 2023

Our aim is to formulate and prove a weak form in equal characteristic

p>0

of the

p

-curvature conjecture. We also show the existence of a counterexample to a strong form of it.
Birational motivic homotopy theories and the slice filtration
Authors: Pelaez Pablo
Published: January 2023

We show that there is an equivalence of categories between the orthogonal components for the slice filtration and the birational motivic stable homotopy categories which are constructed in this paper. Relying on this equivalence, we are able to describe the slices for projective spaces (including

\ P ^{\infty}

), Thom spaces and blow ups.
Cycle classes for $p$-adic étale Tate twists and the image of $p$-adic regulators
Authors: Sato K.
Published: January 2023

In this paper, we construct Chern class maps and cycle class maps with values in

p

-adic étale Tate twists citeS2. We also relate the

p

-adic étale Tate twists with the finite part of Bloch-Kato. As an application, we prove that the integral part of

p

-adic regulator maps has values in the finite part of Galois cohomology under certain assumptions.
Transportation-cost inequalities on path space over manifolds with boundary
Authors: Wang Feng-Yu
Published: January 2023

Let

L=\Delta + Z

for a

C^1

vector field

Z

on a complete Riemannian manifold possibly with a boundary. A number of transportation-cost inequalities on the path space for the (reflecting)

L

-diffusion process are proved to be equivalent to the curvature condition

{Ric}-\nabla Z\ge - K

and the convexity of the boundary (if exists). These inequalities are new even for manifolds without boundary, and are partly extended to non-convex manifolds by using a conformal change of metric which makes the boundary from non-convex to convex.