{"paper":{"title":"Counting periodic points over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Laura Walton","submitted_at":"2017-05-25T03:09:04Z","abstract_excerpt":"Let $V$ be a quasiprojective variety defined over $\\mathbb{F}_q$, and let $\\phi:V\\rightarrow V$ be an endomorphism of $V$ that is also defined over $\\mathbb{F}_q$. Let $G$ be a finite subgroup of $\\operatorname{Aut}_{\\mathbb{F}_q}(V)$ with the property that $\\phi$ commutes with every element of $G$. We show that idempotent relations in the group ring $\\mathbb{Q}[G]$ give relations between the periodic point counts for the maps induced by $\\phi$ on the quotients of $V$ by the various subgroups of $G$. We also show that if $G$ is abelian, periodic point counts for the endomorphism on $V/G$ induc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09034","kind":"arxiv","version":1},"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"}