{"paper":{"title":"Number of irreducible mod l rank 2 sheaves on curves over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chandrashekhar Khare, Gebhard B\\\"ockle","submitted_at":"2016-06-11T18:35:44Z","abstract_excerpt":"Let X be a smooth projective curve of genus g over a finite field F_q of characteristic p. Consider primes l different from p. We formulate some questions related to a well known counting formula of Drinfeld.\n  Drinfeld counts rank 2, irreducible l-adic sheaves on the base change X_n of X to F_{q^n} as n varies. We would like to count rank 2, irreducible mod l sheaves on X_n as n varies. Drinfeld's l-adic count gives an upper bound for the mod l count. We conjecture that Drinfeld's count is the correct asymptotic for the count of rank 2, irreducible mod l sheaves on X_n as n varies with (n,\\el"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03618","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"}