F-signature and Hilbert–Kunz multiplicity : a combined approach and comparison
| Autor: | Kevin Tucker, Thomas Polstra |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
13A35
Pure mathematics 14B05 Algebra and Number Theory Mathematics::Commutative Algebra 010102 general mathematics Local ring Multiplicity (mathematics) $F$-signature Hilbert–Kunz multiplicity Mathematics - Commutative Algebra Commutative Algebra (math.AC) Mathematical proof 01 natural sciences Infimum and supremum Combined approach 0103 physical sciences FOS: Mathematics 13A35 14B05 010307 mathematical physics 0101 mathematics Commutative algebra Mathematics |
| Zdroj: | Algebra Number Theory 12, no. 1 (2018), 61-97 |
| ISSN: | 1944-7833 1937-0652 |
| DOI: | 10.2140/ant.2018.12.61 |
| Popis: | We present a unified approach to the study of Hilbert-Kunz multiplicity, F-signature, 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 F-signature to be viewed as the infimum of relative differences in the Hilbert-Kunz multiplicites of the cofinite ideals in a local ring. Comment: Minor changes and corrections |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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