{"paper":{"title":"Iwasawa Main Conjecture for the Carlitz cyclotomic extension and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Andrea Bandini, Bruno Angl\\`es, Francesc Bars, Ignazio Longhi","submitted_at":"2014-12-18T17:26:44Z","abstract_excerpt":"We prove an Iwasawa Main Conjecture for the class group of the $\\mathfrak{p}$-cyclotomic extension $\\mathcal{F}$ of the function field $\\mathbb{F}_q(\\theta)$ ($\\mathfrak{p}$ is a prime of $\\mathbb{F}_q[\\theta]\\,$), showing that its Fitting ideal is generated by a Stickelberger element. We use this and a link between the Stickelberger element and a $\\mathfrak{p}$-adic $L$-function to prove a close analog of the Ferrero-Washington theorem for $\\mathcal{F}$ and to provide informations on the $\\mathfrak{p}$-adic valuations of the Bernoulli-Goss numbers $\\beta(j)$ (i.e., on the values of the Goss $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5957","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":""},"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"}