Antoine Touzé

Bifunctor cohomology and cohomological finite generation for reductive groups

Let G be a reductive linear algebraic group over a field k. Let A be a finitely generated commutative k-algebra on which G acts rationally by k-algebra automorphisms. Invariant theory states that the ring of invariants AG=H0(G,A) is finitely generated. We show that in fact the full cohomology ring H∗(G,A) is finitely generated. The proof is based on the strict polynomial bifunctor cohomology classes constructed in [22]. We also continue the study of bifunctor cohomology of Γ∗(gl(1))

Lectures on functor homology

Introduction.- A. Djament: Homologie stable des groupes a coefficients polynomiaux.- W. van der Kallen: Lectures on Bifunctors and Finite Generation of Rational Cohomology Algebras.- R. Mikhailov: Polynomial Functors and Homotopy Theory.- A. Touze: Prerequisites of Homological Algebra.