Finite Schur filtration dimension for modules over an algebra with Schur filtration
نویسندگان
چکیده
Let G = GLN or SLN as reductive linear algebraic group over a field k of characteristic p > 0. We prove several results that were previously established only when N ≤ 5 or p > 2 : Let G act rationally on a finitely generated commutative k-algebra A and let grA be the Grosshans graded ring. We show that the cohomology algebra H(G, grA) is finitely generated over k. If moreover A has a good filtration and M is a noetherian A-module with compatible G action, then M has finite good filtration dimension and the H (G,M) are noetherian A-modules. To obtain results in this generality, we employ functorial resolution of the ideal of the diagonal in a product of Grassmannians.
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