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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1606.03618","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-06-11T18:35:44Z","cross_cats_sorted":[],"title_canon_sha256":"158310c9d9efe2a599cb4f30ca3093a4d70f109ba9748ecdc8d5c7f38c112b6e","abstract_canon_sha256":"5b7c88f4912e064feafd11b6691bb89803bb88365bd2d1aefeb9c8548b89956c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:33.519259Z","signature_b64":"sMpGr3VMJoFngfWMaY2fjdZs2gHcBCWfzj6p+2+BKh4eXP/2HwJeMsdCCi+EudZrlaYFC0EpckMMx0DVIfiQCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4166ca71416f23211c17742f6280358ed6292025d0e4dab7685a15df302f8db","last_reissued_at":"2026-05-18T01:12:33.518682Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:33.518682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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