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arXiv · 1802.02793

Local Picard Group of Pointed Monoids and Their Algebras

Davide Alberelli·Holger Brenner
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Abstract

The main goal of this paper is to give an explicit formula for the cohomology of the sheaf of units of the punctured spectrum of a Stanley-Reisner ring. In particular we compute the local Picard group of $K [\triangle]$. To achieve this we study the corresponding purely combinatorial problem on the punctured spectrum of the pointed monoid defined by $\triangle$. The cohomology of the sheaf of units on ${\rm Spec}^ \bullet K[\triangle ]$ is then the direct sum of this combinatorial cohomology, which has a decomposition along the vertices, and another part depending on the field $K$.

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Davide Alberelli, Holger Brenner. 2018-02-08. Local Picard Group of Pointed Monoids and Their Algebras. https://arxiv.org/abs/1802.02793

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