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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("},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1512.04847","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-15T16:41:25Z","cross_cats_sorted":[],"title_canon_sha256":"4a719bfbd1b12c227c052e2874ff854256dbee465b064192ee57839a5c0d5671","abstract_canon_sha256":"d88c08c594c5db415c6dde883af64226d40ecaec6435fdca29d0d985ddd60350"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:34.301418Z","signature_b64":"sPgqgCed25GA03CxrKvIfZGFBG9yB1O+IblBWI6NPym0JhgQr/+gjsLulNlIkAsUbq0+dG/MaqAiG0/aAqA/AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a60385d62d848cd4a3f3a3ae6cab6e00c896d5283b414c97c2ffd8c522b4e5d","last_reissued_at":"2026-05-17T23:53:34.300774Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:34.300774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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