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Half–Exact Coherent Functors over PIDs and Dedekind Domains
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
2016 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

The focus of this thesis is to characterize half–exact coherent functors over principal ideal domains (PIDs) and Dedekind domains. Ever since they where discovered, coherent functors have been useful in the study of some mathematical objects. We aim to explore a little more about them in this thesis.

We first give here a review of the general categorical notions relevant to the characterization. We also review the functors Ext(M,−) and Tor(M,−)  on the category on A–modules, where A is a commutative ring and M is an A–module.

With the assumption that A is a commutative noetherian ring, we introduce coherent functors defined on the category of finitely generated A–modules. It is then shown in the paper that any half–exact coherent functor over a PID, and more generally over a Dedekind domain, arises from a complex of projective modules.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2016. , 40 p.
Series
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1752
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-128616ISBN: 978-91-7685-750-2 (Print)OAI: oai:DiVA.org:liu-128616DiVA: diva2:930732
Presentation
2016-06-08, Nobel (BL32), B-huset, Campus Valla, Linköping, 15:15 (English)
Opponent
Supervisors
Note

The thesis serie title Linköping Studies in Science and Technology. Licentiate Thesis is incorrect. The correct title is Linköping Studies in Science and Technology. Thesis.

Available from: 2016-05-25 Created: 2016-05-25 Last updated: 2016-05-25Bibliographically approved

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