{"paper":{"title":"A remark on the Generalized Hodge Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dario Portelli","submitted_at":"2010-09-27T14:11:52Z","abstract_excerpt":"Let X be a smooth, projective variety over the field of complex numbers. On the space H of its rational cohomology of degree i we have the arithmetic filtration F^p. On the other hand, on the space of cohomology of degree i of X with complex coefficients we have the Hodge filtration G^p. It is well known that F^p is contained in the intersection of G^p with H, and that, in general, this inclusion is strict. In this paper we propose a natural substitute S^p for the Hodge filtration space G^p such that the intersection of S^p with H is the space F^p of the arithmetic filtration. In particular, S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5262","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"}