Cohomology with Grosshans graded coefficients

Details Cohomology with Grosshans graded coefficients Cohomology with Grosshans graded coefficients

2001-08-09

arxiv.org/abs/math/0108066v4

CRM Proceedings and Lecture Notes, Volume 35 (2004), 127-138

Mathematics

Representation Theory

17 pages; correction of twelve subscripts

Scientific paper

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=SL_2 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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