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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 


Authors: Pedro Luis del Angel and Stefan Müller-Stach
Journal: Trans. Amer. Math. Soc. 352 (2000), 1623-1633
MSC (1991): Primary 14C25, 14E10; Secondary 19E15
Published electronically: December 10, 1999
MathSciNet review: 1603890
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Abstract: Let $k$ be a field of characteristic zero. For every smooth, projective $k$-variety $Y$ of dimension $n$ which admits a connected, proper morphism $f: Y \to S$ of relative dimension one, we construct idempotent correspondences (projectors) $\pi _{ij}(Y) \in CH^{n}(Y \times Y,\mathbb{Q})$generalizing a construction of Murre. If $n=3$ and the transcendental cohomology group $H^{2}_{\text{tr}}(Y)$ has the property that $H^{2}_{\text{tr}}(Y,\mathbb{C})=f^{*}H^{2}_{\text{tr}}(S,\mathbb{C})+ {\text{Im... ...(S,\mathbb{C}) \otimes H^{1}(Y,\mathbb{C}) \to H^{2}_{\text{tr}}(Y,\mathbb{C}))$, then we can construct a projector $\pi _{2}(Y)$ which lifts the second Künneth component of the diagonal of $Y$. Using this we prove that many smooth projective 3-folds $X$ over $k$ admit a Chow-Künneth decomposition $\Delta =p_{0}+...+p_{6}$ of the diagonal in $CH^{3}(X \times X,{\mathbb{Q}})$.


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Additional Information

Pedro Luis del Angel
Affiliation: Departamento de Matemáticas, UAM I, Mexico City, Mexico
Address at time of publication: Fachbereich 6, University Essen, 45117, Essen, Germany
Email: pedro.del.angel@uni-essen.de

Stefan Müller-Stach
Affiliation: Fachbereich 6, University Essen, 45117 Essen, Germany
Email: mueller-stach@uni-essen.de

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02302-8
PII: S 0002-9947(99)02302-8
Keywords: Chow group, correspondence, motive, Albanese map
Received by editor(s): September 20, 1997
Published electronically: December 10, 1999
Additional Notes: The first author was supported in part by DFG and CONACYT
The second author was supported in part by DFG
Article copyright: © Copyright 2000 American Mathematical Society