The main goal of the thesis is to give explicit formulas for the computation of the local Picard group of some binoid algebras. In particular the Stanley-Reisner and the general monomial case are covered.
In order to do so, we introduce a new topology on the spectrum of the binoid algebra over a field, that we call combinatorial topology, coarser than Zariski topology, that mimics the topology on the spectrum of a pointed monoid. Then we use the tools of cohomology of sheaves on schemes of pointed monoids in order to prove some formulas for computing the cohomology of the sheaf of units on the punctured spectrum of a simplicial pointed monoid. We prove that the Picard group of a Stanley-Reisner algebra is trivial with the Zariski topology and, finally, we use these results and the combinatorial topology to obtain the explicit formulas.
Lastly, we extend this result to any quotient of the polynomial ring over a monomial ideal.
| Identifer | oai:union.ndltd.org:uni-osnabrueck.de/oai:repositorium.ub.uni-osnabrueck.de:urn:nbn:de:gbv:700-2016102415081 |
| Date | 24 October 2016 |
| Creators | Alberelli, Davide |
| Contributors | Prof. Dr. Holger Brenner, Prof. Dr. Tim Römer |
| Source Sets | Universität Osnabrück |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis |
| Format | application/zip, application/pdf |
| Rights | Namensnennung - Weitergabe unter gleichen Bedingungen 3.0 Unported, http://creativecommons.org/licenses/by-sa/3.0/ |
Page generated in 0.0021 seconds