Dynamics on abelian varieties in positive characteristic

Jakub Byszewski, Gunther Cornelissen, Robert Royals, Thomas Ward

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)2185-2235
Number of pages51
JournalAlgebra and Number Theory
Volume12
Issue number9
DOIs
Publication statusPublished - 21 Dec 2018

Keywords

  • Abelian variety
  • Artin-Mazur zeta function
  • Fixed points
  • Inseparability
  • Natural boundary
  • Recurrence sequence

Cite this