On the motivic cohomology of singular varieties

Federico Binda, Amalendu Krishna

Published 2021-04-16Version 1

We show that for certain singular projective varieties the Levine-Weibel Chow group of 0-cycles coincides with the corresponding Friedlander-Voevodsky motivic cohomology, and that the Chow group of 0-cycles with modulus on a smooth projective variety over a perfect field coincides with the Suslin homology of the complement of the divisor if the latter has normal crossings. Among the applications, we prove several generalizations of the finiteness theorem of Saito and Sato for the Chow group of 0-cycles over $p$-adic fields. We also prove a torsion theorem for Suslin homology which extends a result of Bloch to open varieties.