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Divisibility of Chow groups of 0-cycles 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 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 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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The Cavonius Centre, Gonville and Caius College, University of Cambridge. Faculty of Education, 184 Hills Road, Cambridge, CB2 8PQ, (room GS5 Donald McIntyre Building) Center for Mathematical Sciences, Lecture room MR2

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