Byszewski, J, Cornelissen, G, Royals, R et al. (1 more author) (2018) Dynamics on abelian varieties in positive characteristic. Algebra and Number Theory, 12 (9). pp. 2185-2235. ISSN 1937-0652
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 behaviour is governed by whether or not the action on the local p-torsion group scheme is nilpotent.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018, Mathematical Sciences Publishers. First published in Algebra & Number Theory in Vol. 12 (2018), No. 9, published by Mathematical Sciences Publishers. Reproduced in accordance with the publisher's self-archiving policy. |
Keywords: | abelian variety, inseparability, fixed points, Artin–Mazur zeta function, recurrence sequence, natural boundary |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 23 Jan 2019 11:20 |
Last Modified: | 03 Jan 2020 15:37 |
Published Version: | https://msp.org/ |
Status: | Published |
Publisher: | Mathematical Sciences Publishers |
Identification Number: | 10.2140/ant.2018.12.2185 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:132737 |