The Auslander-Reiten translate on monomial quotient rings

Details The Auslander-Reiten translate on monomial quotient rings The Auslander-Reiten translate on monomial quotient rings

2008-02-20

arxiv.org/abs/0802.2772v3

Advances in Mathematics 226, no. 1, (2011), p. 952-991

Mathematics

Commutative Algebra

35 pages, minor changes and corrections

Scientific paper

10.1016/j.aim.2010.07.006

For a multidegree t in N^n, E.Miller has defined a category of positively t-determined modules over the polynomial ring S in n variables. We consider the Auslander-Reiten translate, Na_t, on the (derived) category of such modules. A monomial ideal I is positively t-determined if every generator x^a has a \leq t. We compute the multigraded cohomology- and betti spaces of Na_t^k(S/I) for every iterate k, and also the S-module structure of these cohomology modules. This comprehensively generalizes results of Hochster and Gr\"abe on local cohomology of Stanley-Reisner rings.

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