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Concept

Groupe de Brauer

Publications associées (10)

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

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

Birational characterization of abelian varieties and ordinary abelian varieties in characteristic p>0

Lei Zhang, Zsolt Patakfalvi

Let k be an algebraically closed field of characteristic p > 0. We give a birational characterization of ordinary abelian varieties over k: a smooth projective variety X is birational to an ordinary abelian variety if and only if kappa(S)(X) = 0 and b(1)(X ...

DUKE UNIV PRESS2019

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

Arithmetic of del Pezzo surfaces of degree 4 and vertical Brauer groups

Anthony Várilly Alvarado

We show that Brauer classes of a locally solvable degree 4 del Pezzo surface X are vertical for some projection away from a plane g : X -> P-1, i.e., that every Brauer class is obtained by pullback from an element of Br k(P-1). As a consequence, we prove t ...

Academic Press Inc Elsevier Science2014

On the Brauer group of diagonal quartic surfaces

We obtain an easy sufficient condition for the Brauer group of a diagonal quartic surface D over Q to be algebraic. We also give an upper bound for the order of the quotient of the Brauer group of D by the image of the Brauer group of Q. The proof is based ...

2011

Diagonal Quartic Surfaces And Transcendental Elements Of The Brauer Group

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

On the Hodge decomposition in $\mathbb{R}^n$

Marc Troyanov

We prove a version of the

L^p

hodge decomposition for differential forms in Euclidean space and a generalization to the class of Lizorkin currents. We also compute the

L_{qp}-

cohomology of

\mathbb{R}^n

. ...

2009

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

Algebraic methods for channel coding

Frédérique Oggier

This work is dedicated to developing algebraic methods for channel coding. Its goal is to show that in different contexts, namely single-antenna Rayleigh fading channels, coherent and non-coherent MIMO channels, algebraic techniques can provide useful tool ...

EPFL2005