Local m-adic constancy of F-pure thresholds and test ideals

Abstract

In this note, we consider a corollary of the ACC conjecture for F-pure thresholds. Specifically, we show that the F-pure threshold (and more generally, the test ideals) associated to a polynomial with an isolated singularity are locally constant in the m-adic topology of the corresponding local ring. As a by-product of our methods, we also describe a simple algorithm for computing all of the F-jumping numbers and test ideals associated to an arbitrary polynomial over an F-finite field.

arXiv comment12 pages, to appear in Mathematical Proceedings of the Cambridge Philosophical Society

References in corpus (6)

• F-thresholds and Bernstein-Sato polynomials
• Shokurov's ACC Conjecture for log canonical thresholds on smooth varieties
• Parameter test ideals of Cohen Macaulay rings
• Test ideals of non-principal ideals: Computations, Jumping Numbers, Alterations and Division Theorems
• ACC for log canonical thresholds
• An algorithm for producing F-pure ideals