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elliptic modular threefold

Journal of K-Theory (1)

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Remarks on Murre's conjecture on Chow groups
Kejian Xu, Ze Xu
Journal:

Journal of K-Theory / Volume 12 / Issue 1 / August 2013

Published online by Cambridge University Press:

30 October 2013, pp. 3-14

Print publication:

August 2013
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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.