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Remarks on Murre's conjecture on Chow groups

Published online by Cambridge University Press:  30 October 2013

Kejian Xu  and
Ze Xu
Kejian Xu
Affiliation:
College of Mathematics, Qingdao University, Qingdao 266071, China, [email protected]
Ze Xu
Affiliation:
Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China, [email protected]
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Abstract

For certain product varieties, Murre's conjecture on Chow groups is investigated. More precisely, let k be an algebraically closed field, X be a smooth projective variety over k and C be a smooth projective irreducible curve over k with function field K. Then we prove that if X (resp. XK) satisfies Murre's conjectures (A) and (B) for a set of Chow-Künneth projectors {, 0 ≤ i ≤ 2dim X} of X (resp. for {()K} of XK) and if for any j, , then the product variety X × C also satisfies Murre's conjectures (A) and (B). As consequences, it is proved that if C is a curve and X is an elliptic modular threefold over k (an algebraically closed field of characteristic 0) or an abelian variety of dimension 3, then Murre's conjecture (B) is true for the fourfold X × C.

Keywords

motivic decompositionChow groupcurveabelian varietyelliptic modular threefold14C25
Type
Research Article
Information
Journal of K-Theory , Volume 12 , Issue 1: Nanjing Special Issue on K-theory, number theory and geometry , August 2013 , pp. 3 - 14
Copyright
Copyright © ISOPP 2013 

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