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We show that the Galois group of $\\phi_N(X)$ over $k(T,g_1,...,g_{r-1})$ is isomorphic to $\\GL_r(\\BF_q[T]/N\\BF_q[T])$, settling a conjecture of Abhyankar."},"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":"1303.2334","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-03-10T16:09:24Z","cross_cats_sorted":[],"title_canon_sha256":"637b4bea6322680b27ca48bdd9da73de2e7369ad2bb75bd6d6a32dd561a0e1a4","abstract_canon_sha256":"7ffeb057aa5f0c280fa39881e7b0ecdf8487d671b0576e612b5313abf1ae308d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:05.331258Z","signature_b64":"A3NfF9wWcIp+uFiVw8ngsxsONN2imcIQsrlP6e5wgVlKGY49xGrX1zDiuCprDlktN8a87XunuBKqrTtokU49Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"346ff363c1f88e2941378822844d612d0cec019bc82df0d73929c0da9c115550","last_reissued_at":"2026-05-18T01:35:05.330644Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:05.330644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Galois groups associated to generic Drinfeld modules and a conjecture of Abhyankar","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Florian Breuer","submitted_at":"2013-03-10T16:09:24Z","abstract_excerpt":"Let $\\phi$ be a rank $r$ Drinfeld $\\BF_q[T]$-module determined by $\\phi_T(X) = TX+g_1X^q+...+g_{r-1}X^{q^{r-1}}+X^{q^r}$, where $g_1,...,g_{r-1}$ are algebraically independent over $\\BF_q(T)$. Let $N\\in\\BF_q[T]$ be a polynomial, and $k/\\BF_q$ an algebraic extension. We show that the Galois group of $\\phi_N(X)$ over $k(T,g_1,...,g_{r-1})$ is isomorphic to $\\GL_r(\\BF_q[T]/N\\BF_q[T])$, settling a conjecture of Abhyankar."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.2334","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1303.2334","created_at":"2026-05-18T01:35:05.330735+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.2334v3","created_at":"2026-05-18T01:35:05.330735+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.2334","created_at":"2026-05-18T01:35:05.330735+00:00"},{"alias_kind":"pith_short_12","alias_value":"GRX7GY6B7CHC","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_16","alias_value":"GRX7GY6B7CHCSQJX","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_8","alias_value":"GRX7GY6B","created_at":"2026-05-18T12:27:45.050594+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GRX7GY6B7CHCSQJXRARIITLBFU","json":"https://pith.science/pith/GRX7GY6B7CHCSQJXRARIITLBFU.json","graph_json":"https://pith.science/api/pith-number/GRX7GY6B7CHCSQJXRARIITLBFU/graph.json","events_json":"https://pith.science/api/pith-number/GRX7GY6B7CHCSQJXRARIITLBFU/events.json","paper":"https://pith.science/paper/GRX7GY6B"},"agent_actions":{"view_html":"https://pith.science/pith/GRX7GY6B7CHCSQJXRARIITLBFU","download_json":"https://pith.science/pith/GRX7GY6B7CHCSQJXRARIITLBFU.json","view_paper":"https://pith.science/paper/GRX7GY6B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.2334&json=true","fetch_graph":"https://pith.science/api/pith-number/GRX7GY6B7CHCSQJXRARIITLBFU/graph.json","fetch_events":"https://pith.science/api/pith-number/GRX7GY6B7CHCSQJXRARIITLBFU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GRX7GY6B7CHCSQJXRARIITLBFU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GRX7GY6B7CHCSQJXRARIITLBFU/action/storage_attestation","attest_author":"https://pith.science/pith/GRX7GY6B7CHCSQJXRARIITLBFU/action/author_attestation","sign_citation":"https://pith.science/pith/GRX7GY6B7CHCSQJXRARIITLBFU/action/citation_signature","submit_replication":"https://pith.science/pith/GRX7GY6B7CHCSQJXRARIITLBFU/action/replication_record"}},"created_at":"2026-05-18T01:35:05.330735+00:00","updated_at":"2026-05-18T01:35:05.330735+00:00"}