{"paper":{"title":"Zero cycles with modulus and zero cycles on singular varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Amalendu Krishna, Federico Binda","submitted_at":"2015-12-15T16:41:25Z","abstract_excerpt":"Given a smooth variety $X$ and an effective Cartier divisor $D \\subset X$, we show that the cohomological Chow group of 0-cycles on the double of $X$ along $D$ has a canonical decomposition in terms of the Chow group of 0-cycles ${\\rm CH}_0(X)$ and the Chow group of 0-cycles with modulus ${\\rm CH}_0(X|D)$ on $X$. When $X$ is projective, we construct an Albanese variety with modulus and show that this is the universal regular quotient of ${\\rm CH}_0(X|D)$.\n  As a consequence of the above decomposition, we prove the Roitman torsion theorem for the 0-cycles with modulus. We show that ${\\rm CH}_0("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04847","kind":"arxiv","version":4},"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"}