Suslin homology via cycles with modulus and applications

Abstract

We show that for a smooth projective variety X X over a field k k and a reduced effective Cartier divisor D ⊂ X D \subset X , the Chow group of 0-cycles with modulus C H 0 ( X | D ) CH_0(X|D) coincides with the Suslin homology H 0 S ( X ∖ D ) H^S_0(X \setminus D) under some necessary conditions on k k and D D . We derive several consequences, and we answer to a question of Barbieri-Viale and Kahn.