{"paper":{"title":"Metric uniformization of morphisms of Berkovich curves via $p$-adic differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Francesco Baldassarri, Velibor Bojkovi\\'c","submitted_at":"2019-01-22T23:23:36Z","abstract_excerpt":"We consider a finite \\'etale morphism $f:Y \\to X$ of quasi-smooth Berkovich curves over a complete nonarchimedean non-trivially valued field $k$, assumed algebraically closed and of characteristic 0, and a skeleton $\\Gamma_f=(\\Gamma_Y,\\Gamma_X)$\n  of the morphism $f$. We prove that $\\Gamma_f$ radializes $f$ if and only if $\\Gamma_X$ controls the pushforward of the constant $p$-adic differential equation $f_*(\\mathcal{O}_Y,d_Y)$.\n  Furthermore, when $f$ is a finite \\'etale morphism of open unit discs, we prove that $f$ is radial if and only if the number of preimages of a point $x\\in X$, counte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07644","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"}