{"paper":{"title":"Even Galois representations and the cohomology of GL(2,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":"2017-02-23T23:14:39Z","abstract_excerpt":"Let $\\rho$ be a two-dimensional even Galois representation which is induced from a character $\\chi$ of odd order of the absolute Galois group of a real quadratic field. After imposing some additional conditions on $\\chi$, we attach $\\rho$ to a Hecke eigenclass in the cohomology of ${\\rm GL}(2,\\mathbb Z)$ with coefficients in a certain infinite-dimensional vector space over a field of characteristic not equal to 2."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07417","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"}