Adic Finiteness: Bounding Homology and Applications
Commutative Algebra
2016-02-25 v2
Abstract
We prove a versions of amplitude inequalities of Iversen, Foxby and Iyengar, and Frankild and Sather-Wagstaff that replace finite generation conditions with adic finiteness conditions. As an application, we prove that a local ring of prime characteristic is regular if and only if for some proper ideal the derived local cohomology complex has finite flat dimension when viewed through some positive power of the Frobenius endomorphism.
Cite
@article{arxiv.1602.03225,
title = {Adic Finiteness: Bounding Homology and Applications},
author = {Sean Sather-Wagstaff and Richard Wicklein},
journal= {arXiv preprint arXiv:1602.03225},
year = {2016}
}
Comments
25 pages. part 3 of a series with arXiv:1401.6925, arXiv:1506.07052, arXiv:1602.03224, arXiv:1602.03226, and arXiv:1602.03227. comments welcome. v.2 has updated references and updated URL for Sather-Wagstaff