{"paper":{"title":"Vanishing Cycles and Wild Monodromy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andrew Obus","submitted_at":"2009-10-05T05:22:26Z","abstract_excerpt":"Let K be a complete discrete valuation field of mixed characteristic (0,p) with algebraically closed residue field, and let f: Y --> P^1 be a three-point G-cover defined over K, where G has a cyclic p-Sylow subgroup P. We examine the stable model of f, in particular, the minimal extension K^{st}/K such that the stable model is defined over K^{st}. Our main result is that, if g(Y) \\geq 2, the ramification indices of f are prime to p, and |P| = p^n, then the p-Sylow subgroup of Gal(K^{st}/K) has exponent dividing p^{n-1}. This extends work of Raynaud in the case that |P| = p."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.0676","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"}