Algebra & Number Theory
- Algebra Number Theory
- Volume 12, Number 1 (2018), 61-97.
$F$-signature and Hilbert–Kunz multiplicity: a combined approach and comparison
We present a unified approach to the study of -signature, Hilbert–Kunz multiplicity, and related limits governed by Frobenius and Cartier linear actions in positive characteristic commutative algebra. We introduce general techniques that give vastly simplified proofs of existence, semicontinuity, and positivity. Furthermore, we give an affirmative answer to a question of Watanabe and Yoshida allowing the -signature to be viewed as the infimum of relative differences in the Hilbert–Kunz multiplicities of the cofinite ideals in a local ring.
Algebra Number Theory, Volume 12, Number 1 (2018), 61-97.
Received: 23 January 2017
Revised: 18 September 2017
Accepted: 31 October 2017
First available in Project Euclid: 4 April 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 13A35: Characteristic p methods (Frobenius endomorphism) and reduction to characteristic p; tight closure [See also 13B22]
Secondary: 14B05: Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx]
Polstra, Thomas; Tucker, Kevin. $F$-signature and Hilbert–Kunz multiplicity: a combined approach and comparison. Algebra Number Theory 12 (2018), no. 1, 61--97. doi:10.2140/ant.2018.12.61. https://projecteuclid.org/euclid.ant/1522807231