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We show that the Galois group of $\\psi_n(X)$ over $k(t,a_1,\\ldots,a_{r-1})$ is isomorphic to $\\mathrm{GL}_r(\\mathbb{F}_q[t]/n\\mathbb{F}_q[t])$, settling a conjecture of Abhyankar. Along the way we obtain an explicit construction of Drinfeld moduli schemes of level $tn$."},"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":"1503.06420","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-22T12:46:31Z","cross_cats_sorted":[],"title_canon_sha256":"5d59a6b1523d83ed3ae032b814f5fd3134bbcde4005e893edf019721bad0a3cd","abstract_canon_sha256":"51c497a10af43aeed446a0204768a402b569c5b8377b1a9271d4bead9aa364ce"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:04.814554Z","signature_b64":"BLDO2Y921MVUNbR45q7ChSp6/fx3tpi2sZCA9889vsIhftJemLkFuI9qzf0r658dOHWYFeIs8ER0Pkv1jM0xAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"964a99ee8ca839503175ec3dc13d435325ea0ac0cf7b8e8b12fd463c44cc8ca8","last_reissued_at":"2026-05-18T01:35:04.813908Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:04.813908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Explicit Drinfeld moduli schemes and Abhyankar's generalized iteration conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Florian Breuer","submitted_at":"2015-03-22T12:46:31Z","abstract_excerpt":"Let $k$ be a field containing $\\mathbb{F}_q$. Let $\\psi$ be a rank $r$ Drinfeld $\\mathbb{F}_q[t]$-module determined by $\\psi_t(X) = tX+a_1X^q+\\cdots+a_{r-1}X^{q^{r-1}}+X^{q^r}$, where $t,a_1,\\ldots,a_{r-1}$ are algebraically independent over $k$. Let $n\\in\\mathbb{F}_q[T]$ be a monic polynomial. We show that the Galois group of $\\psi_n(X)$ over $k(t,a_1,\\ldots,a_{r-1})$ is isomorphic to $\\mathrm{GL}_r(\\mathbb{F}_q[t]/n\\mathbb{F}_q[t])$, settling a conjecture of Abhyankar. 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