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Dynamics on abelian
varieties in positive characteristic
Jakub Byszewski and Gunther CornelissenAppendix: Robert Royals and Thomas Ward |
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Vol. 12 (2018), No. 9, 2185–2235
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Abstract |
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We study periodic points and orbit length distribution for endomorphisms of abelian varieties in characteristic . 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 . The behavior is governed by whether or not the action on the local -torsion group scheme is nilpotent. |
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Keywords
abelian variety, inseparability, fixed points, Artin–Mazur
zeta function, recurrence sequence, natural boundary
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Mathematical Subject Classification 2010
Primary: 37P55
Secondary: 11N45, 14G17, 14K02, 37C25, 37C30
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Milestones
Received: 30 March 2018
Revised: 29 June 2018
Accepted: 29 July 2018
Published: 21 December 2018
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Authors |
| Jakub Byszewski | |
| Wydział Matematyki i
Informatyki Uniwersytet Jagielloński Kraków Poland |
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| Gunther Cornelissen | |
| Mathematisch Instituut University of Utrecht The Netherlands |
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| Robert Royals | |
| School of Mathematics University of East Anglia Norwich United Kingdom |
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| Thomas Ward | |
| Ziff Building University of Leeds United Kingdom |
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