{"paper":{"title":"Arithmetic of critical $p$-adic $L$-functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Denis Benois, K\\^az{\\i}m B\\\"uy\\\"ukboduk","submitted_at":"2024-03-24T09:33:54Z","abstract_excerpt":"Our objective in the present work is to develop a fairly complete arithmetic theory of critical $p$-adic $L$-functions on the eigencurve. To this end, we carry out the following tasks:\n  a) We give an \"\\'etale\" construction of Bella\\\"iche's $p$-adic $L$-functions at a $\\theta$-critical point on the cuspidal eigencurve.\n  b) We introduce the algebraic counterparts of these objects (which arise as appropriately defined Selmer complexes) and develop Iwasawa theory in this context, including a definition of an Iwasawa theoretic $\\mathscr L$-invariant $\\mathscr{L}^{\\rm cr}_{\\rm Iw}$.\n  c) We formul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.16076","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/2403.16076/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"}