{"paper":{"title":"Explicit Estimates for the Number of Rational Points of Singular Complete Intersections over a Finite Field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Guillermo Matera, Mariana P\\'erez, Melina Privitelli","submitted_at":"2014-12-23T17:11:06Z","abstract_excerpt":"Let $V\\subset\\mathbb{P}^n(\\overline{F}_{\\hskip-0.7mm q})$ be a complete intersection defined over a finite field $F_{\\hskip-0.7mm q}$ of dimension $r$ and singular locus of dimension at most $0\\le s\\le r-2$. We obtain an explicit version of the Hooley--Katz estimate $||V(F_{\\hskip-0.7mm q})|-p_r|=\\mathcal{O}(q^{(r+s+1)/2})$, where $|V(F_{\\hskip-0.7mm q})|$ denotes the number of $F_{\\hskip-0.7mm q}$-rational points of $V$ and $p_r:=|\\mathbb{P}^r(F_{\\hskip-0.7mm q})|$. Our estimate improves all the previous estimates in several important cases. Our approach relies on tools of classical algebraic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7446","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"}