Math @ Duke

Publications [#243919] of Ezra Miller
Papers Published
 with Helm, D; Miller, E, Bass numbers of semigroupgraded local cohomology,
Pacific Journal of Mathematics, vol. 209 no. 1
(2003),
pp. 4166 [MR2004c:13028], [math.AG/0010003]
(last updated on 2018/05/27)
Abstract: Given a module M over a ring R that has a grading by a semigroup Q, we present a spectral sequence that computes the local cohomology HIi(M) at any graded ideal I in terms of Ext modules. We use this method to obtain flniteness results for the local cohomology of graded modules over semigroup rings. In particular we prove that for a semigroup Q whose saturation Qsat is simplicial, and a finitely generated module M over k[Q] that is graded by Qgp, the Bass numbers of HIi(M) are finite for any Qgraded ideal I of k[Q]. Conversely, if Qsat is not simplicial, we find a graded ideal I and graded k[Q]module M such that the local cohomology module HIi(M) has infinitedimensional socle. We introduce and exploit the combinatorially defined essential set of a semigroup.


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