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Cohomology with Grosshans graded coefficients. (English) Zbl 1080.20039
Campbell, H. E. A. Eddy (ed.) et al., Invariant theory in all characteristics. Proceedings of the workshop on invariant theory, Queen’s University, Kingston, ON, Canada, April 8–19, 2002. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3244-1/pbk). CRM Proceedings & Lecture Notes 35, 127-138 (2004).
Summary: Let the reductive group \(G\) act on the finitely generated commutative \(k\)-algebra \(A\). We ask if the finite generation property of the ring of invariants \(A^G\) extends to the full cohomology ring \(H^*(G,A)\). We confirm this for \(G=\text{SL}_2\) and also when the action on \(A\) is replaced by the “contracted” action on the Grosshans graded ring \(\text{gr\,}A\), provided the characteristic of \(k\) is large.
For the entire collection see [Zbl 1051.13001].

MSC:
20G10 Cohomology theory for linear algebraic groups
14L24 Geometric invariant theory
14L30 Group actions on varieties or schemes (quotients)
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