Related papers: Brauer equivalent number fields and the geometry o…
In this paper we give a survey of recent methods for the asymptotic and exact enumeration of number fields with given Galois group of the Galois closure. In particular, the case of fields of degree up to 4 is now almost completely solved,…
For algebraic stacks over number fields, we define their Brauer-Manin sets, Brauer-Manin pairings, and extend the descent theory of Colliot-Th\'el\`ene and Sansuc. By extending Sansuc's exact sequence, we show the torsionness of Brauer…
The paper contains a survey of train constructions for infinite symmetric groups and related groups. For certain pairs (a group $G$, a subgroup $K$), we construct categories, whose morphisms are two-dimensional surfaces tiled by polygons…
Spectral equivalences of the quasi-exactly solvable sectors of two classes of Schrodinger operators are established, using Gaudin-type Bethe ansatz equations. In some instances the results can be extended leading to full isospectrality. In…
We consider a quantum integrable inhomogeneous model based on the Brauer algebra B(1) and discuss the properties of its ground state eigenvector. In particular we derive various sum rules, and show how some of its entries are related to…
In this article, we study admissible representations of even unitary groups over local fields, where the quadratic extension is ramified, with invariant vectors under the action of the stabilizer of a unimodular lattice and some properties…
The Brauer-Siegel theorem concerns the size of the product of the class number and the regulator of a number field $K$. We derive bounds for this product in case $K$ is a prime cyclotomic field, distinguishing between whether there is a…
This is a largely expository article based on our previous work on arithmetic diagonal cycles on unitary Shimura varieties. We define a class of Shimura varieties closely related to unitary groups which represent a moduli problem of abelian…
In this paper, we present a conjecture on the degree of unipotent characters in the cohomology of particular Deligne-Lusztig varieties for groups of Lie type, and derive consequences of it. These degrees are a necessary piece of data in the…
A quaternionic field is a pair $p=\{\alpha,u\}$ of function $\alpha$ and vector field $u$ given on a 3d Riemannian maifold $\Omega$ with the boundary. The field is said to be harmonic if $\nabla \alpha={\rm rot\,}u$\, in $\Omega$. The…
The differential Brauer monoid of a differential commutative ring R s defined. Its elements are the isomorphism classes of differential Azumaya R algebras with operation from tensor product subject to the relation that two such algebras are…
There are similarities between algebraic Lie theory and a geometric description of the blocks of the Brauer algebra in characteristic zero. Motivated by this, we study the alcove geometry of a certain reflection group action. We provide…
We show that for nonarchimedean local fields $F$, the pairing from the algebraic part of the Brauer group of a reductive group $G$ characterizes all continuous homomorphisms from $G(F)$ into $\mathbb{Q}/\mathbb{Z}$. This generalizes results…
We establish a uniformization result for metric surfaces - metric spaces that are topological surfaces with locally finite Hausdorff 2-measure. Using the geometric definition of quasiconformality, we show that a metric surface that can be…
While several results have pointed to the existence of exactly quasisymmetric fields on a surface (Garren & Boozer 1991a,b; Plunk & Helander 2018), we have obtained the first such solutions using a vacuum surface expansion formalism. We…
In this article, we compute both the algebraic and the analytic Brauer groups of a homogeneous space under the action of a connected, simply connected, semisimple complex algebraic group, where the stabilizer subgroup is closed and…
We introduce some graded versions of the walled Brauer algebra, working over a field of characteristic zero. This allows us to prove that the walled Brauer algebra is Morita equivalent to an idempotent truncation of a certain infinite…
The aim of this paper is to apply character properties of Frobenius group to a local block form of an group algebra. We start by establishing a block form of Brauer permutation Lemma by using block participation of conjugate classes of a…
We study effective bounds for Brauer groups of Kummer surfaces associated to the Jacobians of curves of genus $2$ defined over number fields.
Given a group $G$ and a number field $K$, the Grunwald problem asks whether given field extensions of completions of $K$ at finitely many places can be approximated by a single field extension of $K$ with Galois group G. This can be viewed…