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Entropy and flatness in local algebraic dynamics
Majidi-Zolbanin, Mahdi
Miasnikov, Nikita
Szpiro, Lucien

Data: 2013
Resum: 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.
Drets: Tots els drets reservats
Llengua: Anglès
Document: article ; recerca ; publishedVersion
Matèria: Local algebraic dynamics ; Local entropy ; Endomorphism of nite length ; Kunz' regularity criterion ; Generalized Hilbert-Kunz multiplicity
Publicat a: Publicacions matemàtiques, Vol. 57, Núm. 2 (2013) , p. 509-544, ISSN 0214-1493

Adreça original:
DOI: 10.5565/PUBLMAT_57213_12
DOI: 10.5565/287163

36 p, 474.0 KB

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