{"paper":{"title":"Selmer group associated to the Chow group of certain codimension two cycles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG","math.KT"],"primary_cat":"math.NT","authors_text":"Kalyan Banerjee, Kalyan Chakraborty","submitted_at":"2019-08-18T11:25:26Z","abstract_excerpt":"Let $X$ be a surface with geometric genus and irregularity zero which is defined over a number field $K$. Let $\\mathscr{X}$ denote a smooth spread of $X$ over the spectrum of a Zariski open subset in the spectrum of the ring of integers and $A^2$ stands for the group of algebraically trivial cycles on schemes modulo rational equivalence. If $j^*: A^2(\\mathscr{X})\\to A^2(X)$ be the flat pull-back corresponding to the embedding $j:X\\hookrightarrow \\mathscr{X}$ then we prove that $\\im(j^*)(K)/A^2(\\mathscr{X})(K)$ is a torsion group. Here $\\im(j^*)(K)$, $A^2(\\mathscr{X})(K)$ stand for the cycles f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06424","kind":"arxiv","version":3},"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/1908.06424/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"}