Graduation Semester and Year
2016
Language
English
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics
Department
Mathematics
First Advisor
Minerva Cordero-Epperson
Second Advisor
David A Jorgensen
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.
Keywords
Support varieties, Rank varieties, Totally acyclic complexes, Realizability, Cohomology
Disciplines
Mathematics | Physical Sciences and Mathematics
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Steele, Nathan Thomas, "Support and Rank Varieties of Totally Acyclic Complexes" (2016). Mathematics Dissertations. 188.
https://mavmatrix.uta.edu/math_dissertations/188
Comments
Degree granted by The University of Texas at Arlington