{"paper":{"title":"Torsions in Cohomology of $\\text{SL}_2(\\mathbb{Z})$ and Congruence of Modular Forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Taiwang Deng","submitted_at":"2019-05-13T19:37:13Z","abstract_excerpt":"We describe torsion classes in the first cohomology group of $\\text{SL}_2(\\mathbb{Z})$. In particular, we obtain generalized Dickson's invariants for p-power polynomial rings. Secondly, we describe torsion classes in the zero-th homology group of $\\text{SL}_2(\\mathbb{Z})$ as a module over the torsion invariants. As application, we obtain various congruences between cuspidal forms of level one and Eisenstein series."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.05260","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"}