{"paper":{"title":"Cohomological nonvanishing for algebraic fundamental groups of ball quotients","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GT","math.NT"],"primary_cat":"math.AG","authors_text":"Matthew Stover","submitted_at":"2025-08-28T14:39:10Z","abstract_excerpt":"Suppose $\\Gamma < \\mathrm{PU}(n,1)$ is a cocompact arithmetic lattice of simplest type with profinite completion $\\widehat{\\Gamma}$. This paper proves there is an open subgroup $\\widehat{\\Gamma}_0 \\le \\widehat{\\Gamma}$ such that $H^j(\\widehat{\\Delta}, \\mathbb{F}_p)$ is nontrivial for every open subgroup ${\\widehat{\\Delta} \\le \\widehat{\\Gamma}_0}$, $j \\le 2n$, and sufficiently large prime $p$. If $n \\ge 2$, nonvanishing is new for all $j \\ge 2$. Consequently, the virtual cohomological dimension of $\\widehat{\\Gamma}$ is at least $2n$, improving the previous lower bound of $1$. The proof shows th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.20847","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.20847/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}