Hostname: page-component-8448b6f56d-mp689 Total loading time: 0 Render date: 2024-04-23T14:57:31.245Z Has data issue: false hasContentIssue false
  • English
  • Français

Hilbert-Kunz Multiplicity and Reduction Mod p

Published online by Cambridge University Press:  11 January 2016

V. Trivedi
V. Trivedi*
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road Mumbai-400005, Indiavija@math.tifr.res.in
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.

We show that the Hilbert-Kunz multiplicities of the reductions to positive characteristics of an irreducible projective curve in characteristic 0 have a well-defined limit as the characteristic tends to infinity.

Keywords

13D4014H6013H15
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 185 , 2007 , pp. 123 - 141
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2007

References

[B1] Brenner, H., The rationality of the Hilbert-Kunz multiplicity in graded dimension two, preprint, arXiv:math.AC/0402180v1.Google Scholar
[B2] Brenner, H., A characteristic zero Hilbert-Kunz criterion for solid closure in dimension two, Math. Res. Lett., 11 (2004), no. 5–6, 563–574.Google Scholar
[BCP] Buchweitz, R., Chen, Q. and Pardue, K., Hilbert-Kunz functions, preprint (Algebraic Geometry e-print series).Google Scholar
[C] Chen, Q., Hilbert-Kunz functions: a survey, unpublished notes May 1997, Essen-Seminar.Google Scholar
[H] Han, C., The Hilbert-Kunz function of a diagonal hypersurface, Ph.D. thesis, Brandeis University (1991).Google Scholar
[HM] Han, C. and Monsky, P., Some surprising Hilbert-Kunz functions, Math. Z., 214 (1993), no. 1, 119–135.Google Scholar
[HN] Harder, G. and Narasimhan, M. S., On the cohomology groups of moduli spaces of vector bundles on curves, Math. Ann., 212 (1975), 215–248.Google Scholar
[L] Langer, A., Semistable sheaves in positive characteristic, Ann. Math., 159 (2004).Google Scholar
[Ma] Maruyama, M., Openness of a family of torsion free sheaves, J. Math. Kyoto Univ., 16-3 (1976), 627–637.Google Scholar
[M] Monsky, P., The Hilbert-Kunz function, Math. Ann., 263 (1983), 43–49.Google Scholar
[SB] Shepherd-Barron, N. I., Semistability and reduction mod p, Topology, 37 (1998), no. 3, 659–664.Google Scholar
[T1] Trivedi, V., Semistabiltiy and HK multiplicities for curves, J. of algebra, 284 (2005), 627–644.Google Scholar
[T2] Trivedi, V., Strong semistability and Hilbert-Kunz multiplicity for singular plane curves, to appear in Contemporary Mathematics of AMS.Google Scholar
[WY] Watanabe, K. and Yoshida, K., Hilbert-Kunz multiplicity and an inequality between multiplicity and colength, J. Algebra, 230 (2000), 295–317.Google Scholar