Asymptotic Prime Divisors Related to Ext, Regularity of Powers of Ideals, and Syzygy Modules
arXiv:1709.05881
Abstract
This dissertation focuses on the following topics: (1) asymptotic prime divisors over complete intersection rings, (2) asymptotic stability of complexities over complete intersection rings, (3) asymptotic linear bounds of Castelnuovo-Mumford regularity in multigraded modules, and (4) characterizations of regular local rings via syzygy modules of the residue field.
Ph.D Thesis, Indian Institute of Technology Bombay, 2016, contains results from arXiv:1403.6972, arXiv:1405.5970 and arXiv:1511.08012