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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0910.0676","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-10-05T05:22:26Z","cross_cats_sorted":[],"title_canon_sha256":"fe13fe5b369926fc829fde9d3a62de4f888dc006ef877e25cc89a8de14091014","abstract_canon_sha256":"4fb3793f7754196bacf8ffef502ded0dc3ad82fc40e9e546c5aa5d2ab124389e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:05.612232Z","signature_b64":"FaYGqUvohswCyDeO3zJI7kJk2eWW+To5mkpTD2VmQcA1vKQrQDN/IwcQz+368s5xtjAj0+d9o7DkqpgUrNZjBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3eb1c93e72df02af322d977427093bf5f4599d5020af17fee10e15ca8f4027d8","last_reissued_at":"2026-05-18T03:46:05.611487Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:05.611487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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