{"paper":{"title":"Rational Singularities and Rational Points","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"H\\'el\\`ene Esnault, Manuel Blickle","submitted_at":"2006-01-06T21:03:23Z","abstract_excerpt":"If $X$ is a projective, geometrically irreducible variety defined over a finite field $\\F_q$, such that it is smooth and its Chow group of 0-cycles fulfills base change, i.e. $CH_0(X\\times_{\\F_q}\\bar{\\F_q(X)})=\\Q$, then the second author's theorem asserts that its number of rational points satisfies $|X(\\F_q)| \\equiv 1$ modulo $q$. If $X$ is not smooth, this is no longer true. Indeed J. Koll\\'ar constructed an example of a rationally connected surface over $\\F_q$ without any rational points. Based on the work by Berthelot-Bloch and the second author computing the slope $<1$ piece of rigid coho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0601131","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"}