Concept

Algèbre d'Azumaya

Publications associées (12)

NORM TORI OF ETALE ALGEBRAS AND UNRAMIFIED BRAUER GROUPS

Let k be a field, and let L be an etale k-algebra of finite rank. If a is an element of k(x), let X-a be the affine variety defined by N-L/k(x) = a. Assuming that L has at least one factor that is a cyclic field extension of k, we give a combinatorial desc ...

Hebrew Univ Magnes Press2023

On the Grothendieck-Serre conjecture for classical groups

Eva Bayer Fluckiger

We prove some new cases of the Grothendieck-Serre conjecture for classical groups. This is based on a new construction of the Gersten-Witt complex for Witt groups of Azumaya algebras with involution on regular semilocal rings, with explicit second residue ...

WILEY2022

Orders That Are Etale-Locally Isomorphic

Eva Bayer Fluckiger, Mathieu Huruguen

Let R be a semilocal Dedekind domain with fraction field F. It is shown that two hereditary R-orders in central simple F-algebras that become isomorphic after tensoring with F and with some faithfully flat etale R-algebra are isomorphic. On the other hand, ...

AMER MATHEMATICAL SOC2020

Orders that are étale-locally isomorphic

Eva Bayer Fluckiger, Mathieu Huruguen

Let R be a semilocal Dedekind domain with fraction field F. It is shown that two hereditary R-orders in central simple F-algebras that become isomorphic after tensoring with F and with some faithfully flat étale R-algebra are isomorphic. On the other hand, ...

2019

Hasse principles for multinorm equations

Eva Bayer Fluckiger, Ting-Yu Lee

A classical result of Hasse states that the norm principle holds for finite cyclic extensions of global fields, in other words local norms are global norms. We investigate the norm principle for finite dimensional commutative kale algebras over global fiel ...

2019

Embedding functor for classical groups and Brauer–Manin obstruction

Eva Bayer Fluckiger, Ting-Yu Lee

Let K be a global field of characteristic not 2. The embedding problem for maximal tori in a classical group G can be described in terms of algebras with involution. The aim of this paper is to give an explicit description of the obstruction group to the H ...

2015

Hermitian Forms over Algebras with Involution and Hermitian Categories

Daniel Arnold Moldovan

This thesis is concerned with the algebraic theory of hermitian forms. It is organized in two parts. The first, consisting of the first two chapters, deals with some descent properties of unimodular hermitian forms over central simple algebras with involut ...

EPFL2012

Diagonal Quartic Surfaces And Transcendental Elements Of The Brauer Group

Evis Ieronymou

We exhibit central simple algebras over the function field of a diagonal quartic surface over the complex numbers that represent the 2-torsion part of its Brauer group. We investigate whether the 2-primary part of the Brauer group of a diagonal quartic sur ...

Cambridge University Press2010

Singularities of generic characteristic polynomials and smooth finite splittings of Azumaya algebras over surfaces

Manuel Ojanguren

Let k be an algebraically closed field. Let P(X-11,...,X-nn, T) be the characteristic polynomial of the generic matrix (X-ij) over k. We determine its singular locus as well as the singular locus of its Galois splitting. If X is a smooth quasi-projective s ...

Springer-Verlag2009

Euclidean minima and central division algebras

Eva Bayer Fluckiger, Jérôme Chaubert

The notion of Euclidean minimum of a number field is a classical one. In this paper we generalize it to central division algebras and establish some general results in this new context. ...

2009