Cohomological Invariant Theory
Speaker: Professor Wilberd van der Kallen (Universiteit Utrecht)
Date: Wed 22nd October 2008
Location: Mathematical Sciences Seminar Room
The ''first fundamental theorem" of invariant theory goes back to the 19th century. Nowadays one says that if a reductive algebraic group acts algebraically on a finitely generated commutative k-algebra, then the ring of invariants H^0(G,A) is also a finitely generated k-algebra. Here k is the ground field. We have conjectured that more generally for any geometrically reductive group scheme G acting on A, the full cohomology ring H^*(G,A) is finitely generated. This generalizes theorems of Evens (1961) and of Friedlander-Suslin (1997). This summer the conjecture was proved by Antoine Touze, just before his thesis defence. As the proofs are long, we will mostly discuss the context (and the meaning of the terms).
(This talk is part of the K-Theory, Quadratic Forms and Number Theory series.)