Exterior products of zero-cycles

Matt Kerr
2006 Journal für die Reine und Angewandte Mathematik  
Citation for published item: uerrD wF @PHHTA 9ixterior produts of zeroEylesF9D tournl f¤ ur die reine und ngewndte wthemtikF a grelles journlFD THH F ppF IEPQF Further information on publisher's website: httpXGGdxFdoiForgGIHFISISGgivviFPHHTFHVR Publisher's copyright statement: Additional information: Use policy The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or
more » ... ucational, or not-for-prot purposes provided that: • a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders. Please consult the full DRO policy for further details. Abstract. We study the exterior product CH 0 ðX Þ n CH 0 ðY Þ ! CH 0 ðX  Y Þ on 0-cycles modulo rational equivalence. The main tools used are higher cycle-and Abel-Jacobi-classes developed in [L1] and [K2]. The theorem of [RS] (applied to 0-cycles) appears as a special case of our results. Z A Z p ðX Þ is denoted by hZi A CH p ðX Þ (to distinguish from its fundamental class ½Z A Hom MHS À QðÀpÞ; H 2p ðX ; QÞ Á ). Brought to you by | University of Durham Authenticated | 129.234.252.66 Download Date | 3/18/14 5:48 PM 2 Kerr, Exterior products of zero-cycles Brought to you by | University of Durham Authenticated | 129.234.252.66 Download Date | 3/18/14 5:48 PM This paper was written at the University of Chicago and MPIM-Bonn; we wish to thank both institutions for their hospitality. We also thank J. Lewis and the referee for comments which have led to improvements in the exposition. 3 Kerr, Exterior products of zero-cycles Brought to you by | University of Durham Authenticated | 129.234.252.66 Download Date | 3/18/14 5:48 PM ! ! JðH V Þ l JðH 2 Þ in which the square commutes and pr V i V is the identity. From (c), ðpr V pr 1 ÞðXÞ ¼ x and ðpr 2 pr 1 ÞðXÞ ¼ 0; hence pr 1 ðXÞ ¼ i V ðxÞ. If (i) holds, then JðH V Þ l JðH 1 X G 0 Þ ,! JðH 1 Þ and so b 1 cannot kill i V ðxÞ; we conclude that b 0 ðXÞ 3 0. 6 Kerr, Exterior products of zero-cycles Brought to you by | University of Durham Authenticated | 129.234.252.66 Download Date | 3/18/14 5:48 PM K
doi:10.1515/crelle.2006.084 fatcat:nzdzjg65dvelfh2pkvp5ocfphu