Suslin homology via cycles with modulus and applications

Binda, Federico; Krishna, Amalendu

doi:10.1090/tran/8815

Suslin homology via cycles with modulus and applications
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Trans. Amer. Math. Soc. 376 (2023), 1445-1473 Request permission

Abstract:

We show that for a smooth projective variety $X$ over a field $k$ and a reduced effective Cartier divisor $D \subset X$, the Chow group of 0-cycles with modulus $CH_0(X|D)$ coincides with the Suslin homology $H^S_0(X \setminus D)$ 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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