{"paper":{"title":"Stabilization indices of potentially Mumford curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andrew Obus, Daniele Turchetti","submitted_at":"2021-12-29T18:35:45Z","abstract_excerpt":"Let $X$ be a smooth projective curve over a complete discretely valued field $K$. Let $L/K$ be the minimal extension such that $X \\times_K L$ has a semi-stable model, and write $e(L/K)$ for the ramification index of $L/K$. Let $e(X)$ be the so-called ``stabilization index'' of $X$, defined by Halle and Nicaise as the lcm of the multiplicities of the ``principal'' irreducible components of a minimal regular snc-model of $X$.\n  It is known that if $L/K$ is tame, then $e(X) = e(L/K)$. If one drops the tameness assumption, but instead assumes that $X$ has index one and potentially multiplicative r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.14728","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2112.14728/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}