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arXiv · 2211.10577

Graded local cohomology of modules over semigroup rings

Byeongsu Yu·Laura Felicia Matusevich
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Abstract

We give a combinatorial description of local cohomology modules of a graded module over a semigroup ring, with support at the graded maximal ideal. This combinatorial framework yields Hochster-type formulas for the Hilbert series of such local cohomology modules in terms of the homology of finitely many polyhedral cell complexes. A Cohen--Macaulay criterion immediately follows. We also provide an alternative proof of a result of [18] characterizing Cohen--Macaulay affine semigroup rings.

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Byeongsu Yu, Laura Felicia Matusevich. 2022-11-19. Graded local cohomology of modules over semigroup rings. https://arxiv.org/abs/2211.10577

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