University of Cambridge > Talks.cam > Number Theory Seminar > Divisibility of Chow groups of 0-cycles of varieties over local fields with algebraically closed residue fields

Divisibility of Chow groups of 0-cycles of varieties over local fields with algebraically closed residue fields

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(Joint work with H. Esnault.) Let X be a smooth projective variety defined over the maximal unramified extension of a p-adic field. S. Saito and K. Sato have proved that the Chow group of zero-cycles of degree 0 on X up to rational equivalence is an extension of a finite group by a p’-divisible group. We study this finite group and show in particular that it vanishes for simply connected surfaces with geometric genus zero, as well as for K3 surfaces with semi-stable reduction if p=0, but that it does not vanish for arbitrary simply connected surfaces. In particular, the cycle class map to ├ętale cohomology with finite (prime to p) coefficients need not be injective.

This talk is part of the Number Theory Seminar series.

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