{"paper":{"title":"Algebraic solutions of differential equations over the projective line minus three points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Yunqing Tang","submitted_at":"2014-12-26T01:16:48Z","abstract_excerpt":"The Grothendieck--Katz $p$-curvature conjecture predicts that an arithmetic differential equation whose reduction modulo $p$ has vanishing $p$-curvatures for {\\em almost all} $p,$ has finite monodromy. It is known that it suffices to prove the conjecture for differential equations on $\\mathbb{P}^{1}-\\{0,1,\\infty\\}.$ We prove a variant of this conjecture for $\\mathbb{P}^{1}-\\{0,1,\\infty\\},$ which asserts that if the equation satisfies a certain convergence condition for {\\em all} $p,$ then its monodromy is trivial. For those $p$ for which the $p$-curvature makes sense, its vanishing implies our"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7875","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"}