Divisibility of Chow groups of 0cycles of varieties over local fields with algebraically closed residue fields
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If you have a question about this talk, please contact Tom Fisher.
(Joint work with H. Esnault.) Let X be a smooth projective variety defined
over the maximal unramified extension of a padic field. S. Saito and
K. Sato have proved that the Chow group of zerocycles 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 semistable reduction if p=0, but that it does not vanish for
arbitrary simply connected surfaces. In particular, the cycle class map to
étale 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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