We show that for a smooth projective variety X over a field k and a reduced effective Cartier divisor D subset of X, the Chow group of 0-cycles with modulus CH0(X divide D) coincides with the Suslin homology H0S (X set minus D) under some necessary conditions on k and D. We derive several consequences, and we answer to a question of Barbieri-Viale and Kahn.
Suslin homology via cycles with modulus and applications / F. Binda, A. Krishna. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 376:2(2023 Feb), pp. 1445-1473. [10.1090/tran/8815]
Suslin homology via cycles with modulus and applications
F. Binda;
2023
Abstract
We show that for a smooth projective variety X over a field k and a reduced effective Cartier divisor D subset of X, the Chow group of 0-cycles with modulus CH0(X divide D) coincides with the Suslin homology H0S (X set minus D) under some necessary conditions on k and D. We derive several consequences, and we answer to a question of Barbieri-Viale and Kahn.
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