{"paper":{"title":"Galois Representations Associated to $p$-adic Families of Modular Forms of Finite Slope","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.NT","authors_text":"Tomoki Mihara","submitted_at":"2015-04-18T14:54:15Z","abstract_excerpt":"We define a pro-$p$ Abelian sheaf on a modular curve of a fixed level $N \\geq 5$ divisible by a prime number $p \\neq 2$. Every $p$-adic representation of $\\text{Gal}(\\overline{\\mathbb{Q}}/\\mathbb{Q})$ associated to an eigenform is obtained as a quotient of its \\'etale cohomology. For any compact $\\mathbb{Z}_p[[1 + N \\mathbb{Z}_p]]$-algebra $\\Lambda_1$ satisfying certain suitable conditions, we construct a representation of $\\text{Gal}(\\overline{\\mathbb{Q}}/\\mathbb{Q})$ over $\\Lambda_1$ associated to a $\\Lambda_1$-adic cuspidal eigenform of finite slope as a scalar extension of a quotient of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04728","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"}