{"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"}