{"paper":{"title":"Twisted limit formula for torsion and cyclic base change","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.NT","authors_text":"Michael Lipnowski, Nicolas Bergeron","submitted_at":"2014-09-23T20:32:54Z","abstract_excerpt":"Let $G$ be the group of complex points of a real semi-simple Lie group whose fundamental rank is equal to 1, e.g. $G= \\SL_2 (\\C) \\times \\SL_2 (\\C)$ or $\\SL_3 (\\C)$. Then the fundamental rank of $G$ is $2,$ and according to the conjecture made in \\cite{BV}, lattices in $G$ should have 'little' --- in the very weak sense of 'subexponential in the co-volume' --- torsion homology. Using base change, we exhibit sequences of lattices where the torsion homology grows exponentially with the \\emph{square root} of the volume.\n  This is deduced from a general theorem that compares twisted and untwisted $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6749","kind":"arxiv","version":2},"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"}