[Projecteurs de Chow–Künneth pour des variétés modulaires]
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.
Accepté le :
Publié le :
B.Brent Gordon 1 ; Masaki Hanamura 2 ; Jacob P. Murre 3
@article{CRMATH_2002__335_9_745_0, author = {B.Brent Gordon and Masaki Hanamura and Jacob P. Murre}, title = {Chow{\textendash}K\"unneth projectors for modular varieties}, journal = {Comptes Rendus. Math\'ematique}, pages = {745--750}, publisher = {Elsevier}, volume = {335}, number = {9}, year = {2002}, doi = {10.1016/S1631-073X(02)02506-2}, language = {en}, }
B.Brent Gordon; Masaki Hanamura; Jacob P. Murre. Chow–Künneth projectors for modular varieties. Comptes Rendus. Mathématique, Volume 335 (2002) no. 9, pp. 745-750. doi : 10.1016/S1631-073X(02)02506-2. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02506-2/
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