Cohomology with Grosshans graded coefficients

2001/08/31 by Wilberd van der Kallen
Mathematics · #math.RT #msc:20G10

paper · pdf

published as CRM Proceedings and Lecture Notes, Volume 35 (2004), 127-138 · 17 pages; correction of twelve subscripts

arxiv created 2004/06/24 · arxiv updated 2009/11/30

Abstract

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 rational cohomology ring H^*(G,A). We confirm this when G=SL₂ and also when the characteristic of k is large and the action on A is replaced by the `contracted' action on the Grosshans graded ring gr(A). In the printed version of this paper the first level of some spectral sequences was misidentified as the second. This affects twelve subscripts. We have corrected them (in 3.10, 4.11, 4.12).

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