Stability: index and order in the Brauer group

Brauer Algebras and the Brauer Group

An algebra is a vector space V over a field k together with a kbilinear product of vectors under which V is a ring. A certain class of algebras, called Brauer algebras algebras which split over a finite Galois extension appear in many subfields of abstract algebra, including K-theory and class field theory. Beginning with a definition of the the tensor product, we define and study Brauer algebr...

Groupoids and the Brauer Group

Using a groupoid of matrix subalgebras in a fixed matrix algebra we define some nonabelian bundle gerbe which probably gives rise to some new twistings in K-theory.

The Differential Brauer Group

The Brauer group and indecomposable (2,1)-cycles

We show that the torsion in the group of indecomposable (2, 1)-cycles on a smooth projective surface over an algebraically closed field is isomorphic to a twist of its Brauer group, away from the characteristic. This is more generally true for any smooth projective variety under some hypotheses. In particular, this group is infinite as soon as b2−ρ > 0. We derive a new insight into Rǒıtman’s th...

Period and Index in the Brauer Group of an Arithmetic Surface

This paper consists of two parts: in the first, we use the deformation theory of twisted sheaves on stacks to generalize results of de Jong and Saltman on the period-index problem for the Brauer group, yielding various new cases of the standard conjecture. In the second part, we use the geometric techniques of the first part to relate the Hasse principle for certain smooth projective geometrica...