{"paper":{"title":"Hasse-Weil Zeta Functions Modulo a Prime","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chris Hall","submitted_at":"2026-06-03T18:28:57Z","abstract_excerpt":"Let $\\mathbb{F}_q$ be a finite field of characteristic $p$ and $\\pi\\colon Y\\to X$ be a finite $\\mathbb{F}_q$-morphism of separated $\\mathbb{F}_q$-schemes of finite type. Suppose $\\pi$ is generically Galois with group $G$ of prime order $r\\neq p$. We determine the mod-$r$ reduction of the zeta function of $Y$ in terms of the zeta function of $X$ and the branch locus $Z\\subset X$ of $\\pi$. We give applications to curves and to numerators of hyperelliptic/superelliptic curves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.05340","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.05340/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}