The cohomology rings of rank 3 simple groups are Cohen-Macaulay
英文摘要：
In this paper we show that the mod 2 cohomology ring of any finite simple group of rank 3 or less (at the prime 2) must be Cohen-Macaulay.
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The Cohen-Macaulay property in derived commutative algebra
By extending some basic results of Grothendieck and Foxby about local cohomology to commutative DG-rings, we prove new amplitude inequalities about finite DG-modules of finite injective dimension over commutative local DG-rings, complementing results of Jørgensen and resolving a recent conjecture of Minamoto. When these inequalities are equalities, we arrive to the notion of a local-Cohen-Macaulay DG-ring. We make a detailed study of this notion, showing that much of the classical theory of Cohen-Macaulay rings and modules can be generalized to the derived setting, and that there are many natu…
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