4 A reductive group with finitely generated cohomology algebras .
نویسنده
چکیده
Let G be the linear algebraic group SL3 over a field k of characteristic two. Let A be a finitely generated commutative k-algebra on which G acts rationally by k-algebra automorphisms. We show that the full cohomology ring H(G,A) is finitely generated. This extends the finite generation property of the ring of invariants AG. We discuss where the problem stands for other geometrically reductive group schemes.
منابع مشابه
2 4 Ju n 20 04 A reductive group with finitely generated cohomology algebras
Let G be the linear algebraic group SL3 over a field k of characteristic two. Let A be a finitely generated commutative k-algebra on which G acts rationally by k-algebra automorphisms. We show that the full cohomology ring H(G,A) is finitely generated. This extends the finite generation property of the ring of invariants AG. We discuss where the problem stands for other geometrically reductive ...
متن کاملA reductive group with finitely generated cohomology algebras
Let G be the linear algebraic group SL3 over a field k of characteristic two. Let A be a finitely generated commutative k-algebra on which G acts rationally by k-algebra automorphisms. We show that the full cohomology ring H∗(G, A) is finitely generated. This extends the finite generation property of the ring of invariants AG. We discuss where the problem stands for other geometrically reductiv...
متن کامل2 00 5 A reductive group with finitely generated cohomology algebras .
Let G be the linear algebraic group SL3 over a field k of characteristic two. Let A be a finitely generated commutative k-algebra on which G acts rationally by k-algebra automorphisms. We show that the full cohomology ring H(G,A) is finitely generated. This extends the finite generation property of the ring of invariants AG. We discuss where the problem stands for other geometrically reductive ...
متن کاملBifunctor Cohomology and Cohomological Finite Generation for Reductive Groups
LetG be a reductive linear algebraic group over a field k. LetA be a finitely generated commutative k-algebra on which G acts rationally by k-algebra automorphisms. Invariant theory states that the ring of invariantsA = H 0(G,A) is finitely generated. We show that in fact the full cohomology ringH ∗(G,A) is finitely generated. The proof is based on the strict polynomial bifunctor cohomology cla...
متن کاملRepresentation Dimension and Finitely Generated Cohomology
We consider selfinjective Artin algebras whose cohomology groups are finitely generated over a central ring of cohomology operators. For such an algebra, we show that the representation dimension is strictly greater than the maximal complexity occurring among its modules. This provides a unified approach to computing lower bounds for the representation dimension of group algebras, exterior alge...
متن کامل