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

Published online by Cambridge University Press:  02 May 2017

DANIEL J. HERNÁNDEZ ,
LUIS NÚÑEZ-BETANCOURT  and
EMILY E. WITT
DANIEL J. HERNÁNDEZ
Affiliation:
University of Kansas, Department of Mathematics, 405 Snow Hall, 1460 Jayhawk Blvd, Lawrence, KS 66045–7594, USA. e-mail: [email protected]
LUIS NÚÑEZ-BETANCOURT
Affiliation:
Centro de Investigación en Matemáticas, A.C., Jalisco S/N, Col. Valenciana CP: 36023 Guanajuato, Gto, Mexico, Apartado Postal 402, CP 36000. e-mail: [email protected]
EMILY E. WITT
Affiliation:
University of Kansas, Department of Mathematics, 405 Snow Hall, 1460 Jayhawk Blvd, Lawrence, KS 66045–7594, USA. e-mail: [email protected]
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Abstract

In this paper, 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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 164 , Issue 2 , March 2018 , pp. 285 - 295
Copyright
Copyright © Cambridge Philosophical Society 2017 

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References

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