Brauer Groups of Linear Algebraic Groups with Characters

Brauer Groups of Linear Algebraic Groups with Characters

Let G be a connected linear algebraic group over an algebraically closed field of characteristic zero. Then the Brauer group of G is shown to be C X (Q/Z)<n) where C is finite and n = d(d l)/2, with d the Z-Ta.nk of the character group of G. In particular, a linear torus of dimension d has Brauer group (Q/Z)(n) with n as above. In [6], B. Iversen calculated the Brauer group of a connected, char...

Brauer Groups

I define the Brauer group of a field k as similarity classes of central simple algebras over k. Then I introduce non-abelean cohomology and use it to prove that the Brauer group is isomorphic to a certain cohomology group. Brauer groups show up in global class field theory.

Linear Algebraic Groups

Linear Algebraic Groups

Linear Algebraic Groups

We give a summary, without proofs, of basic properties of linear algebraic groups, with particular emphasis on reductive algebraic groups.