Linear algebraic groups with good reduction

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.

Linear Algebraic Groups

These are the exercises (with solutions) and the exam for the course Algebra II, winter term 2014/2015 at Bonn. Students were not assumed to have heard algebraic geometry before, just algebra. In particular, basic affine and projective geometry were introduced from scratch. The course covered the standard material up to the structure results about maximal tori and Borel subgroups. Root systems ...

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...