Chow–Künneth projectors for modular varieties
[Projecteurs de Chow–Künneth pour des variétés modulaires]
Gordon, B.Brent1 ; Hanamura, Masaki2 ; Murre, Jacob P.3
1 Department of Mathematics, University of Oklahoma, 601 Elm, Room 423, Norman, OK 73019, USA
2 Graduate School of Mathematics, Kyushu University, Fukuoka, 812 Japan
3 Department of Mathematics, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands
Comptes Rendus. Mathématique, Tome 335 (2002) no. 9, pp. 745-750.

Nous démontrons l'existence des projecteurs de Chow–Künneth pour certaines variétés, incluant les variétés de Kuga–Shimura des variétés modulaires de Hilbert. Les projecteurs de Chow–Künneth d'une variété lisse projective sont par définition des idempotents orthogonaux de l'anneau de Chow des auto-correspondances qui donnent la décomposition par les degrés de la cohomologie totale de la variété.

We show the existence of the Chow–Künneth projectors for certain varieties, including Kuga–Shimura varieties of Hilbert modular varieties. The Chow–Künneth projectors of a smooth projective variety are, by definition, mutually orthogonal idempotents of the Chow ring of self-correspondences which give decomposition of the total cohomology of the variety into degree pieces.

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DOI : 10.1016/S1631-073X(02)02506-2
Gordon, B.Brent 1 ; Hanamura, Masaki 2 ; Murre, Jacob P. 3

1 Department of Mathematics, University of Oklahoma, 601 Elm, Room 423, Norman, OK 73019, USA
2 Graduate School of Mathematics, Kyushu University, Fukuoka, 812 Japan
3 Department of Mathematics, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands 
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Gordon, B.Brent; Hanamura, Masaki; Murre, Jacob P. Chow–Künneth projectors for modular varieties. Comptes Rendus. Mathématique, Tome 335 (2002) no. 9, pp. 745-750. doi : 10.1016/S1631-073X(02)02506-2. http://www.numdam.org/articles/10.1016/S1631-073X(02)02506-2/

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