Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-10T10:02:15.119Z Has data issue: false hasContentIssue false
  • English
  • Français

Estimates for F-jumping numbers and bounds for Hartshorne–Speiser–Lyubeznik numbers

Published online by Cambridge University Press:  11 January 2016

Mircea Mustaţă  and
Wenliang Zhang
Mircea Mustaţă
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA, mmustata@umich.edu
Wenliang Zhang*
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA
*
Department of Mathematics, University of Nebraska, Lincoln, NE 68588-0130, USA, wzhang15@unl.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Given an ideal a on a smooth variety in characteristic zero, we estimate the F-jumping numbers of the reductions of a to positive characteristic in terms of the jumping numbers of a and the characteristic. We apply one of our estimates to bound the Hartshorne–Speiser–Lyubeznik invariant for the reduction to positive characteristic of a hypersurface singularity.

Keywords

13A3514B1514F18
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 210 , June 2013 , pp. 133 - 160
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2013

References

[AIM] American Institute of Mathematics, AIM problem lists: Test ideals and multiplier ideals, http://aimpl.org/testandmultiplierideals Google Scholar
[BHMM] Bhatt, B., Hernández, D. J., Miller, L. E., and Mustaţă, M., Log canonical thresholds, F-pure thresholds, and nonstandard extensions, Algebra Number Theory 6 (2013), 1459–1482.Google Scholar
[Bli] Blickle, M., The intersection homology D-module in finite characteristic, Ph.D. dissertation, University of Michigan, Ann Arbor, Michigan, 2001. MR 2702619.Google Scholar
[BMS1] Blickle, M., Mustaţă, M., and Smith, K. E., Discreteness and rationality of F-thresholds, Michigan Math. J. 57 (2008), 43–61. MR 2492440. DOI 10.1307/mmj/1220879396.Google Scholar
[BMS2] Blickle, M., Mustaţă, M., and Smith, K. E., F-thresholds of hypersurfaces, Trans. Amer. Math. Soc. 361, no. 12 (2009), 6549–6565. MR 2538604. DOI 10.1090/S0002-9947-09-04719-9.Google Scholar
[Gra] Granville, A., “Arithmetic properties of binomial coefficients, I: Binomial coefficients modulo prime powers” in Organic Mathematics (Burnaby, 1995), CMS Conf. Proc. 20, Amer. Math. Soc., Providence, 1997, 253–276. MR 1483922.Google Scholar
[Hara] Hara, N., A characterization of rational singularities in terms of injectivity of Frobenius maps, Amer. J. Math. 120 (1998), 981–996. MR 1646049.Google Scholar
[HY] Hara, N. and Yoshida, K.-I., A generalization of tight closure and multiplier ideals, Trans. Amer. Math. Soc. 355, no. 8 (2003), 3143–3174. MR 1974679. DOI 10.1090/S0002-9947-03-03285-9.Google Scholar
[HS] Hartshorne, R. and Speiser, R., Local cohomological dimension in characteristic p, Ann. of Math. (2) 105 (1977), 45–79. MR 0441962.Google Scholar
[Kat] Katzman, M., Parameter-test-ideals of Cohen-Macaulay rings, Compos. Math. 144 (2008), 933–948. MR 2441251. DOI 10.1112/S0010437X07003417.Google Scholar
[Laz] Lazarsfeld, R., Positivity in Algebraic Geometry, II: Positivity for Vector Bundles, and Multiplier Ideals, Ergeb. Math. Grenzgeb. (3) 49, Springer, Berlin, 2004. MR 2095472. DOI 10.1007/978-3-642-18808-4.Google Scholar
[Lyu] Lyubeznik, G., F-modules: Applications to local cohomology and D-modules in characteristic p > 0, J. Reine Angew. Math. 491 (1997), 65–130. MR 1476089. DOI 10.1515/crll.1997.491.65.Google Scholar
[MS] Mustaţă, M. and Srinivas, V., Ordinary varieties and the comparison between multiplier ideals and test ideals, Nagoya Math. J. 204 (2011), 125–157. MR 2863367.Google Scholar
[Sha] Sharp, R. Y., On the Hartshorne-Speiser-Lyubeznik theorem about Artinian modules with a Frobenius action, Proc. Amer. Math. Soc. 135 (2007), 665–670. MR 2262861. DOI 10.1090/S0002-9939-06-08606-0.Google Scholar
[TW] Takagi, S. and Watanabe, K.-i., On F-pure thresholds, J. Algebra 282 (2004), 278–297. MR 2097584. DOI 10.1016/j.jalgebra.2004.07.011.Google Scholar