{"paper":{"title":"Higher Newton polygons and integral bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"E. Nart, J. Guardia, J. Montes","submitted_at":"2009-02-19T18:29:06Z","abstract_excerpt":"Let $A$ be a Dedekind domain, $K$ the fraction field, $\\p$ a non-zero prime ideal of $A$, and $K_\\pp$ the completion of $K$ with respect to the $\\p$-adic topology. At the input of a monic irreducible separable polynomial, $f(x)\\in A[x]$, Montes algorithm determines the factorization of $f(x)$ over $K_\\pp[x]$, and it provides essential arithmetic information about the finite extensions of $K_\\pp$ determined by the different irreducible factors. In particular, it can be used to compute $\\p$-integral bases of the extension of $K$ determined by $f(x)$ \\cite{newapp}. In this paper we present new (a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.3428","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"}