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$F$-signature and
Hilbert–Kunz multiplicity: a combined approach and
comparison
Thomas Polstra and Kevin Tucker |
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Vol. 12 (2018), No. 1, 61–97
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Abstract |
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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. |
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Keywords
$F$-signature, Hilbert–Kunz multiplicity
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Mathematical Subject Classification 2010
Primary: 13A35
Secondary: 14B05
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Milestones
Received: 23 January 2017
Revised: 18 September 2017
Accepted: 31 October 2017
Published: 13 March 2018
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Authors |
| Thomas Polstra | |
| Department of Mathematics University of Utah Salt Lake City, UT United States |
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| Kevin Tucker | |
| Department of Mathematics University of Illinois at Chicago Chicago, IL United States |
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