{"paper":{"title":"Equivariant Torsion and Base Change","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Michael Lipnowski","submitted_at":"2013-12-09T18:38:59Z","abstract_excerpt":"What is the true order of growth of torsion in the cohomology of an arithmetic group? Let $D$ be a quaternion over an imaginary quadratic field $F.$ Let $E/F$ be a cyclic Galois extension with $\\mathrm{Gal}(E/F) = \\langle \\sigma \\rangle.$ We prove lower bounds for \"the Lefschetz number of $\\sigma$ acting on torsion cohomology\" of certain Galois-stable arithmetic subgroups of $D_E^\\times.$ For these same subgroups, we unconditionally prove a would-be-numerical consequence of the existence of a hypothetical base change map for torsion cohomology."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2540","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"}