English

Continuity of Hilbert-Kunz multiplicity and F-signature

Commutative Algebra 2019-12-11 v4

Abstract

We establish the continuity of Hilbert-Kunz multiplicity and F-signature as functions from a Cohen-Macaulay local ring (R,\m,k)(R,\m,k) of prime characteristic to the real numbers at reduced parameter elements with respect to the \m\m-adic topology.

Keywords

Cite

@article{arxiv.1707.04366,
  title  = {Continuity of Hilbert-Kunz multiplicity and F-signature},
  author = {Thomas Polstra and Ilya Smirnov},
  journal= {arXiv preprint arXiv:1707.04366},
  year   = {2019}
}

Comments

New version: as pointed out by Alessandro De Stefani the main theorem for F-signature holds only if the ring is Gorenstein