{"paper":{"title":"Some mixed Hodge structure on l^2-cohomology of covering of K\\\"ahler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Pascal Dingoyan","submitted_at":"2010-06-14T18:01:19Z","abstract_excerpt":"We give methods to compute l^2-cohomology groups of a covering manifolds obtained by removing pullback of a (normal crossing) divisor to a covering of a compact K\\\"ahler manifold. We prove that in suitable quotient categories, these groups admit natural mixed Hodge structure whose graded pieces are given by expected Gysin maps."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.2784","kind":"arxiv","version":3},"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"}