{"paper":{"title":"Morphisms of Berkovich curves and the different function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Adina Cohen, Dmitri Trushin, Michael Temkin","submitted_at":"2014-08-13T09:10:39Z","abstract_excerpt":"Given a generically \\'etale morphism $f\\colon Y\\to X$ of quasi-smooth Berkovich curves, we define a different function $\\delta_f\\colon Y\\to[0,1]$ that measures the wildness of the topological ramification locus of $f$. This provides a new invariant for studying $f$, which cannot be obtained by the usual reduction techniques. We prove that $\\delta_f$ is a piecewise monomial function satisfying a balancing condition at type 2 points analogous to the classical Riemann-Hurwitz formula, and show that $\\delta_f$ can be used to explicitly construct the simultaneous skeletons of $X$ and $Y$. As an app"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2949","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"}