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SUMMARY:Divisibility of Chow groups of 0-cycles of varieties over local fi
 elds with algebraically closed residue fields - Olivier Wittenberg (ENS\, 
 Paris)
DTSTART:20120313T143000Z
DTEND:20120313T153000Z
UID:TALK35220@talks.cam.ac.uk
CONTACT:Tom Fisher
DESCRIPTION:(Joint work with H. Esnault.)  Let X be a smooth projective va
 riety defined\nover the maximal unramified extension of a p-adic field.  S
 . Saito and\nK. Sato have proved that the Chow group of zero-cycles of deg
 ree 0 on X up\nto rational equivalence is an extension of a finite group b
 y a p'-divisible\ngroup.  We study this finite group and show in particula
 r that it vanishes\nfor simply connected surfaces with geometric genus zer
 o\, as well as for K3\nsurfaces with semi-stable reduction if p=0\, but th
 at it does not vanish for\narbitrary simply connected surfaces.  In partic
 ular\, the cycle class map to\nétale cohomology with finite (prime to p) 
 coefficients need not be\ninjective.\n
LOCATION:MR13
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