{"paper":{"title":"Endomorphism rings of reductions of Drinfeld modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Mihran Papikian, Sumita Garai","submitted_at":"2018-04-21T06:53:19Z","abstract_excerpt":"Let $A=\\mathbb{F}_q[T]$ be the polynomial ring over $\\mathbb{F}_q$, and $F$ be the field of fractions of $A$. Let $\\phi$ be a Drinfeld $A$-module of rank $r\\geq 2$ over $F$. For all but finitely many primes $\\mathfrak{p}\\lhd A$, one can reduce $\\phi$ modulo $\\mathfrak{p}$ to obtain a Drinfeld $A$-module $\\phi\\otimes\\mathbb{F}_\\mathfrak{p}$ of rank $r$ over $\\mathbb{F}_\\mathfrak{p}=A/\\mathfrak{p}$. The endomorphism ring $\\mathcal{E}_\\mathfrak{p}=\\mathrm{End}_{\\mathbb{F}_\\mathfrak{p}}(\\phi\\otimes\\mathbb{F}_\\mathfrak{p})$ is an order in an imaginary field extension $K$ of $F$ of degree $r$. Let $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07904","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"}