{"paper":{"title":"Dynamics on abelian varieties in positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DS"],"primary_cat":"math.NT","authors_text":"Gunther Cornelissen, Jakub Byszewski, Robert Royals, Thomas Ward","submitted_at":"2018-02-21T16:54:35Z","abstract_excerpt":"We study periodic points for endomorphisms $\\sigma$ of abelian varieties $A$ over algebraically closed fields of positive characteristic $p$. We show that the dynamical zeta function $\\zeta_\\sigma$ of $\\sigma$ is either rational or transcendental, the first case happening precisely when $\\sigma^n-1$ is a separable isogeny for all $n$. We call this condition very inseparability and show it is equivalent to the action of $\\sigma$ on the local $p$-torsion group scheme being nilpotent.\n  The \"false\" zeta function $D_\\sigma$, in which the number of fixed points of $\\sigma^n$ is replaced by the degr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07662","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}