Dynamics on abelian varieties in positive characteristic

Byszewski, Jakub, Cornelissen, Gunther, Royals, Robert and Ward, Thomas (2018) Dynamics on abelian varieties in positive characteristic. Algebra and Number Theory, 12 (9). pp. 2185-2235. ISSN 1937-0652

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Abstract

We study periodic points and orbit length distribution for endomorphisms of abelian varieties in characteristic p > 0. We study rationality, algebraicity and the natural boundary property for the dynamical zeta function (the latter using a general result on power series proven by Royals and Ward in the appendix), as well as analogues of the prime number theorem, also for tame dynamics, ignoring orbits whose order is divisible by p. The behavior is governed by whether or not the action on the local p-torsion group scheme is nilpotent.

Item Type: Article
Uncontrolled Keywords: abelian variety,artin-mazur zeta function,fixed points,inseparability,natural boundary,recurrence sequence,algebra and number theory ,/dk/atira/pure/subjectarea/asjc/2600/2602
Faculty \ School: Faculty of Science > School of Mathematics
Related URLs:
Depositing User: LivePure Connector
Date Deposited: 25 Mar 2019 10:30
Last Modified: 02 Sep 2019 10:32
URI: https://ueaeprints.uea.ac.uk/id/eprint/70331
DOI: 10.2140/ant.2018.12.2185

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