{"paper":{"title":"Reducible Galois representations and the homology of GL(3,Z)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Avner Ash, Darrin Doud","submitted_at":"2012-05-14T16:35:05Z","abstract_excerpt":"We prove the following theorem: Let $\\bar\\F_p$ be an algebraic closure of a finite field of characteristic $p$. Let $\\rho$ be a continuous homomorphism from the absolute Galois group of $\\Q$ to $\\GL(3,\\bar\\F_p)$ which is isomorphic to a direct sum of a character and a two-dimensional odd irreducible representation. Under the condition that the conductor of $\\rho$ is squarefree, we prove that $\\rho$ is attached to a Hecke eigenclass in the homology of an arithmetic subgroup $\\Gamma$ of $\\GL(3,\\Z)$. In addition, we prove that the coefficient module needed is, in fact, predicted by a conjecture o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3086","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"}