Suslin homology via cycles with modulus and applications

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 ${\mathrm{CH}}_0(X|D)$ coincides with the Suslin homology $H_0^S(X\setminus D)$ under some necessary conditions on $k$ and $D$. We derive several consequences, and we answer to a question of Barbieri-Viale and Kahn.

27 pages. Final version, to appear in Transactions of the AMS