Ascending chain condition for $F$-pure thresholds on a fixed strongly $F$-regular germ
Algebraic Geometry
2019-05-29 v4 Commutative Algebra
Abstract
In this paper, we prove that the set of all -pure thresholds on a fixed germ of a strongly -regular pair satisfies the ascending chain condition. As a corollary, we verify the ascending chain condition for the set of all -pure thresholds on smooth varieties or, more generally, on varieties with tame quotient singularities, which is an affirmative answer to a conjecture given by Blickle, Musta\c{t}\v{a} and Smith.
Cite
@article{arxiv.1710.05331,
title = {Ascending chain condition for $F$-pure thresholds on a fixed strongly $F$-regular germ},
author = {Kenta Sato},
journal= {arXiv preprint arXiv:1710.05331},
year = {2019}
}
Comments
28pages; v3: corrected Lemma 2.19; fixed several typos and minor errors; v4: minor changes