{"paper":{"title":"Algebraic equations on the adelic closure of a Drinfeld module","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.LO"],"primary_cat":"math.NT","authors_text":"Dragos Ghioca, Thomas Scanlon","submitted_at":"2010-12-08T18:51:18Z","abstract_excerpt":"Let $k$ be a field of positive characteristic and $K = k(V)$ a function field of a variety $V$ over $k$ and let ${\\mathbf A}_K$ be a ring of ad\\'{e}les of $K$ with respect to a cofinite set of the places on $K$ corresponding to the divisors on $V$. Given a Drinfeld module $\\Phi:{\\mathbb F}[t] \\to \\operatorname{End}_K({\\mathbb G}_a)$ over $K$ and a positive integer $g$ we regard both $K^g$ and ${\\mathbf A}_K^g$ as $\\Phi({\\mathbb F}_p[t])$-modules under the diagonal action induced by $\\Phi$. For $\\Gamma \\subseteq K^g$ a finitely generated $\\Phi(\\F_p[t])$-submodule and an affine subvariety $X \\su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1825","kind":"arxiv","version":1},"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"}