Zero cycles on singular varieties and their desingularisations

Abstract

We use pro cdh-descent of $K$-theory [the author, J. Inst. Math. Jussieu 15, No. 3, 539--567 (2016; Zbl 1366.19005)] to study the relationship between the zero cycles on a singular variety $X$ and those on its desingularisation $X^{\prime }$. We prove many cases of a conjecture of S. Bloch and V. Srinivas, and relate the Chow groups of $X$ to the Kerz-Saito Chow group with modulus of $X^{\prime }$ relative to its exceptional fibre.