Zero cycles on singular varieties and their desingularisations

  • Matthew Morrow

    Mathematisches Institut Universität Bonn Endenicher Allee 60 53115 Bonn, Germany


We use pro cdh-descent of KK-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 XX and those on its desingularisation XX'. We prove many cases of a conjecture of S. Bloch and V. Srinivas, and relate the Chow groups of XX to the Kerz-Saito Chow group with modulus of XX' relative to its exceptional fibre.