“Serre's Conjecture”, for the most part of the second half of the 20th century,-ferred to the
famous statement made by J.-P. Serre in 1955, to the effect that one did not know if? nitely …

Consider a connected reductive group G over a number field F. For technical reasons we
assume that the derived group of G is simply connected (see [L1]). in [L3] Langlands partially …

A purity conjecture due to Grothendieck and Auslander–Goldman predicts that the Brauer
group of a regular scheme does not change after removing a closed subscheme of …

For a homogeneous spaceX (not necessarily principal) of a connected algebraic group G
(not necessarily linear) over a number field k, we prove a theorem of strong approximation …

The central theme of this book is the study of rational points on algebraic varieties of Fano
and intermediate type--both in terms of when such points exist and, if they do, their …

We show that for complex analytic K 3 surfaces any torsion class in H 2 (X, OX∗) comes from
an Azumaya algebra. In other words, the Brauer group equals the cohomological Brauer …

One of the most important tools for studying Brauer proups of fields is Galois cohomology.
Group theoretic information about Gal (ks/k) or various properties of the Galois cohomology …

Given a field $ F $, one may ask which finite groups are Galois groups of field extensions $
E/F $ such that $ E $ is a maximal subfield of a division algebra with center $ F $. This …

We show that, in general, over a regular integral noetherian affine scheme X of dimension at
least 6, there exist Brauer classes on X for which the associated division algebras over the …

As the title suggests, this paper will touch on a variety of topics connected with Galois
cohomology and the Brauer group. The basic situation is the following. Let G be a finite …