Binda, Federico and Krishna, Amalendu (2018) Zero cycles with modulus and zero cycles on singular varieties. COMPOSITIO MATHEMATICA, 154 (1). pp. 120-187. ISSN 0010-437X, 1570-5846
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Given a smooth variety X and an effective Cartier divisor D subset of 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 CH0(X) and the Chow group of 0-cycles with modulus CH0(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 CH0(X|D). As a consequence of the above decomposition, we prove the Roitman torsion theorem for the 0-cycles with modulus. We show that CH0(X|D) is torsion-free and there is an injective cycle class map CH0(X|D) hooked right arrow K-0(X, D) if X is affine. For a smooth affine surface X, this is strengthened to show that K-0(X, D) is an extension of CH1(X|D) by CH0(X|D).
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | HIGHER CHOW GROUPS; ROITMANS THEOREM; ALBANESE VARIETIES; K-THEORY; 0-CYCLES; TORSION; COMPLEX; FIELD; algebraic cycles; Chow groups; singular schemes; cycles with modulus |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 24 Mar 2020 08:24 |
| Last Modified: | 24 Mar 2020 08:24 |
| URI: | https://pred.uni-regensburg.de/id/eprint/15499 |
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