{"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. Along the way we obtain an explicit construction of Drinfeld moduli schemes of level $tn$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06420","kind":"arxiv","version":2},"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"}