Zero cycles on singular varieties and their desingularisations

Abstract

We use pro cdh-descent of $K$-theory 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.

Remark 2.8 added, explaining applications to class field theory of singular surfaces over finite fields. To appear in Documenta Mathematica, extra volume