Local Picard group of pointed monoids and their algebras

The main goal of this article is to give an explicit formula for in terms of simplicial and reduced simplicial cohomology, where is the Stanley-Reisner ring of the simplicial complex △. In particular, we compute the local Picard group of . To achieve this, we study the corresponding purely combinato...

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Bibliographic Details
Published in:Communications in algebra 2019-06, Vol.47 (6), p.2308-2340
Main Authors: Alberelli, Davide, Brenner, Holger
Format: Article
Language:English
Subjects:
Apexes
Combinatorial analysis
Homology
Monoids
Picard group
simplicial complex
Stanley-Reisner rings
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Summary:The main goal of this article is to give an explicit formula for in terms of simplicial and reduced simplicial cohomology, where is the Stanley-Reisner ring of the simplicial complex △. In particular, we compute the local Picard group of . To achieve this, we study the corresponding purely combinatorial problem on the punctured spectrum of the pointed monoid defined by △. The cohomology of the sheaf of units on is then the direct sum of this combinatorial cohomology, which has a decomposition along the vertices, and another part depending on the field .
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2018.1492592