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By Mr (i: J (d, David J. [benson and David John (-aber


On the regularity conjecture for the cohomology of finite groups. (English summary) Proc. Edinb. Math. Soc. (2) 51 (2008), no. 2, 273–284. Let k be a field of characteristic p, G a finite group and m the maximal ideal of the cohomology ring H ∗ (G, k) consisting of the positive degree elements. Given a graded H ∗ (G, k)-module M, the m-torsion of M, denoted ΓmM, is the submodule {m ∈ M | there exists n ≥ 1 such that m n m = 0} of M. The functor Γm is left exact, and its right derived functors Hi m(M) give the local cohomology of M. Since M is graded, its local cohomology is internally graded. Hence one can define the (extended) integer a i m(M) def = sup{j ∈ Z | H i,j m (M) = 0}. The Castelnuovo-Mumford regularity of M, denoted Reg M, is defined as Reg M = sup{a i m(M) + i}. The author has conjectured that Reg H ∗ (G, k) = 0 for every finite group G. In this paper, h

Year: 2013
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