Zero Cycles on Singular Varieties and Their Desingularisations

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.

2010 Mathematics Subject Classification: 14C35

Keywords and Phrases: Zero cycles; $K$-theory; singular varieties.

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