{"paper":{"title":"Sur les composantes connexes d'une famille d'espaces analytiques p-adiques","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"J\\'er\\^ome Poineau","submitted_at":"2014-01-10T12:36:06Z","abstract_excerpt":"Let $X=\\mathcal{M}(A)$ be an affinoid space and let $f,g \\in A$. We study the sets of connected components of the spaces defined by an inequality of the form $|f|\\le r|g|$, with $r\\ge 0$. We prove that there exists a finite partition of $\\mathbb{R}_+$ into intervals where those sets are canonically in bijection and that the bounds of those intervals belong to $\\sqrt{\\rho(A)}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2311","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"}