| Date: |
2013 |
| Abstract: |
For a local endomorphism of a noetherian local ring we introduce a notion of entropy, along with two other asymptotic invariants. We use this notion of entropy to extend numerical conditions in Kunz' regularity criterion to every contracting endomorphism of a noetherian local ring, and to give a characteristic-free interpretation of the definition of Hilbert-Kunz multiplicity. We also show that everyfinite endomorphism of a complete noetherian local ring of equal characteristic can be lifted to afinite endomorphism of a complete regular local ring. The local ring of an algebraic or analytic variety at a pointfixed by afinite self-morphism inherits a local endomorphism whose entropy is well-defined. This situation arises at the vertex of the fine cone over a projective variety with a polarized self-morphism, where we compare entropy with degree. |
| Rights: |
Tots els drets reservats.  |
| Language: |
Anglès |
| Document: |
Article ; recerca ; Versió publicada |
| Subject: |
Local algebraic dynamics ;
Local entropy ;
Endomorphism of nite length ;
Kunz' regularity criterion ;
Generalized Hilbert-Kunz multiplicity |
| Published in: |
Publicacions matemàtiques, Vol. 57, Núm. 2 (2013) , p. 509-544, ISSN 2014-4350 |
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