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dc.contributor.advisor | Jorgensen, David A. | |
dc.creator | Steele, Nathan Thomas | |
dc.date.accessioned | 2016-10-25T19:24:25Z | |
dc.date.available | 2016-10-25T19:24:25Z | |
dc.date.created | 2016-08 | |
dc.date.issued | 2016-08-12 | |
dc.date.submitted | August 2016 | |
dc.identifier.uri | http://hdl.handle.net/10106/26121 | |
dc.description.abstract | Support and rank varieties of modules over a group algebra of an elementary abelian p-group have been well studied. In particular, Avrunin and Scott showed that in this setting, the rank and support varieties are equivalent. Avramov and Buchweitz proved an analogous result for pairs of modules over arbitrary commutative local complete intersection rings. In this dissertation we study support and rank varieties in the triangulated category of totally acyclic chain complexes over a complete intersection ring and show that these varieties are also equivalent. We also show that any homogeneous affine variety is realizable as the support of some pair of totally acyclic complexes. | |
dc.format.mimetype | application/pdf | |
dc.language.iso | en_US | |
dc.subject | Support varieties | |
dc.subject | Rank varieties | |
dc.subject | Totally acyclic complexes | |
dc.subject | Realizability | |
dc.subject | Cohomology | |
dc.title | Support and Rank Varieties of Totally Acyclic Complexes | |
dc.type | Thesis | |
dc.contributor.committeeMember | Cordero-Epperson, Minerva | |
dc.degree.department | Mathematics | |
dc.degree.name | Doctor of Philosophy in Mathematics | |
dc.date.updated | 2016-10-25T19:26:32Z | |
thesis.degree.department | Mathematics | |
thesis.degree.grantor | The University of Texas at Arlington | |
thesis.degree.level | Doctoral | |
thesis.degree.name | Doctor of Philosophy in Mathematics | |
dc.type.material | text | |
dc.creator.orcid | 0000-0002-6494-2481 | |
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