{"paper":{"title":"\\bs{p}-Adic Confluence of $\\bs{q}$-Difference Equations","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrea Pulita","submitted_at":"2006-12-27T20:57:26Z","abstract_excerpt":"We develop the theory of $p$-adic confluence of $q$-difference equations. The main result is the surprising fact that, in the $p$-adic framework, a function is solution of a differential equation if and only if it is solution of a $q$-difference equation. This fact implies an equivalence, called ``Confluence'', between the category of differential equations and those of $q$-difference equations. We obtain this result by introducing a category of ``sheaves'' on the disk $\\mathrm{D}^-(1,1)$, whose stalk at 1 is a differential equation, the stalk at $q$ is a $q$-difference equation if $q$ is not "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612729","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"}