{"paper":{"title":"Bounded functions on the character variety","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Konstantin Ardakov, Laurent Berger","submitted_at":"2023-01-31T14:08:31Z","abstract_excerpt":"This paper is motivated by an open question in $p$-adic Fourier theory, that seems to be more difficult than it appears at first glance. Let $L$ be a finite extension of $\\mathbb{Q}_p$ with ring of integers $o_L$ and let $\\mathbb{C}_p$ denote the completion of an algebraic closure of $\\mathbb{Q}_p$. In their work on $p$-adic Fourier theory, Schneider and Teitelbaum defined and studied the character variety $\\mathfrak{X}$. This character variety is a rigid analytic curve over $L$ that parameterizes the set of locally $L$-analytic characters $\\lambda : (o_L,+) \\to (\\mathbb{C}_p^\\times,\\times)$. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.13650","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2301.13650/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}