{"paper":{"title":"Iwasawa theory of overconvergent modular forms, I: Critical $p$-adic $L$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David Hansen","submitted_at":"2015-08-17T11:36:02Z","abstract_excerpt":"We construct an Euler system of $p$-adic zeta elements over the eigencurve which interpolates Kato's zeta elements over all classical points. Applying a big regulator map gives rise to a purely algebraic construction of a two-variable $p$-adic $L$-function over the eigencurve. As a first application of these ideas, we prove the equality of the $p$-adic $L$-functions associated with a critical-slope refinement of a modular form by the works of Bella\\\"iche/Pollack-Stevens and Kato/Perrin-Riou."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03982","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":""},"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"}