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arXiv · 1801.08207

Modules of infinite regularity over commutative graded rings

Luigi Ferraro
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Abstract

In this work, we prove that if a graded, commutative algebra $R$ over a field $k$ is not Koszul then, denoting by $\mathfrak{m}$ the maximal homogeneous ideal of $R$ and by $M$ a finitely generated graded $R$-module, the nonzero modules of the form $\mathfrak{m} M$ have infinite Castelnuovo-Mumford regularity. We also prove that over complete intersections which are not Koszul, a nonzero direct summand of a syzygy of $k$ has infinite regularity. Finally, we relate the vanishing of the graded deviations of $R$ to having a nonzero direct summand of a syzygy of $k$ of finite regularity.

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Luigi Ferraro. 2018-01-24. Modules of infinite regularity over commutative graded rings. https://arxiv.org/abs/1801.08207

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