{"paper":{"title":"Topology of higher Albanese maps and aspherical varieties with nilpotent fundamental group","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Vasily Rogov","submitted_at":"2026-07-21T11:54:39Z","abstract_excerpt":"Let $X$ be a normal complex algebraic variety. Let $\\mathcal{G}^s_{\\mathbb{Z}}(X)$ be the maximal torsion free nilpotent quotient of $\\pi_1(X)$ of nilpotency class at most $s$. Let $F^{\\bullet}\\mathfrak{g}^s$ be the Morgan--Hain Hodge filtration on the Lie algebra of the $s$-th lower central quotient of the complex Malcev completion of $\\pi_1(X)$. We show that the natural map $H^k(\\mathcal{G}^s_{\\mathbb{Z}}(X), \\mathbb{Z}) \\to H^k(X, \\mathbb{Z})$ vanishes for $k > \\dim F^1\\mathfrak{g}^s$. If $\\mathcal{G}^s_{\\mathbb{Z}}(X)$ is of nilpotency class greater than two, this includes the top nonvanis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19013","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/2607.19013/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"}