{"paper":{"title":"Conductors of wild extensions of local fields, especially in mixed characteristic (0,2)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrew Obus","submitted_at":"2011-09-22T11:31:56Z","abstract_excerpt":"If K_0 is the fraction field of the Witt vectors over an algebraically closed field k of characteristic p, we calculate upper bounds on the conductor of higher ramification for (the Galois closure of) extensions K_0(zeta_{p^r}, sqrt[p^r]{a})/K_0, where a is in K_0(zeta_{p^r}). Here zeta_{p^r} is a primitive p^r-th root of unity. In certain cases, including when a is in K_0 and p=2, we calculate the conductor exactly. These calculations can be used to determine the discriminants of various extensions of Q obtained by adjoining roots of unity and radicals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4776","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"}