Local Picard Group of Pointed Monoids and Their Algebras

2018/02/08 by Alberelli, Davide, Brenner, Holger
#13C20 #13F55 #14C22 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1802.02793

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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