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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 $"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1409.6749","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-23T20:32:54Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"53b14be668097d490836eab41605741e0b9935f5ba57226eaedd09c4804ccc74","abstract_canon_sha256":"f7297a3d6e028986668dbcb37588e1b50f19c9b67d820cf5b0da691a54c6686b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:22.303585Z","signature_b64":"ZZ1AZiOAxNrVUJNZ+LoJXH/0xCAFJs6viz4oDb1IrGsL67ccK/2nIWGSVxfS9wnR5wuc+V4ABZe35sD543EEDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"373f51dc52761af491cfaf9deae773e616a7a8f0e95cc3cc9407f7ccbf9d87b4","last_reissued_at":"2026-05-18T01:19:22.302967Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:22.302967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\SL_3 (\\C)$. 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