Zero cycles on singular varieties and their desingularisations

TL;DR

This paper investigates the relationship between zero cycles on singular varieties and their desingularisations using pro cdh-descent of K-theory, proving cases of a conjecture and relating Chow groups with modulus.

Contribution

It introduces a novel approach using pro cdh-descent to connect zero cycles on singular varieties with those on their desingularisations, proving new cases of a conjecture.

Findings

Proves many cases of a conjecture of Bloch and Srinivas.

Relates Chow groups of singular varieties to Kerz--Saito Chow groups with modulus.

Establishes a link between 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 $X'$. 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 $X'$ relative to its exceptional fibre.