5 papers · 1 filter
A theorem about maximal Cohen-Macaulay modules
Thomas Polstra
It is shown in a local strongly -regular ring there exits natural number so that if is any finitely generated maximal Cohen-Macaulay module then the pushforward of …
Equimultiplicity Theory of Strongly -regular rings
Thomas Polstra, Ilya Smirnov
We explore the equimultiplicity theory of the -invariants Hilbert--Kunz multiplicity, -signature, Frobenius Betti numbers, and Frobenius Euler characteristic over strongly $F…
Global Frobenius Betti numbers and F-splitting ratio
Alessandro De Stefani, Thomas Polstra, Yongwei Yao
We extend the notion of Frobenius Betti numbers and F-splitting ratio to large classes of finitely generated modules over rings of prime characteristic, which are not assumed to be…
Nilpotence of Frobenius actions on local cohomology and Frobenius closure of ideals
Thomas Polstra, Pham Hung Quy
The study of Frobenius actions on local cohomology modules over a local ring of prime characteristic has interesting connections with the theory of tight closure. This paper establ…
Depths and Cohen-Macaulay Properties of Path Ideals
Daniel Campos, Ryan Gunderson, Susan Morey +2
Given a tree T on n vertices, there is an associated ideal I of a polynomial ring in n variables over a field, generated by all paths of a fixed length of T. We show that such an i…