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.
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.
Accepted:
Published online:
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/
[1] Smooth Compactification of Locally Symmetric Varieties, Math. Sci. Press, 1975
[2] Faisceaux Pervers, Analyse et topologie sur les espaces singuliers, Astérisque, Volume 100 (1982), pp. 7-171
[3] Intersection Cohomology, Prog. in Math., 50, Birkhäuser, 1984 (pp. 47–182)
[4] A. Corti, M. Hanamura, Motivic decomposition and intersection Chow groups I, Preprint
[5] Motivic decomposition of abelian schemes and the Fourier transform, J. Reine Angew. Math., Volume 422 (1991), pp. 201-219
[6] Intersection Theory, Springer, 1984
[7] Intersection homology II, Inv. Math., Volume 71 (1983), pp. 77-129
[8] Chow motives of elliptic modular surfaces and threefolds, Report W 96-16, Math. Institut, Univ. of Leiden, 1996
[9] Chow motives of elliptic modular threefolds, J. Reine Angew. Math., Volume 514 (1999), pp. 145-164
[10] Standard conjectures on algebraic cycles, Algebraic Geometry, Bombay Colloquium, Oxford, 1969, pp. 193-199
[11] S. Kleiman, Algebraic cycles and Weil conjectures, Dix Exposés sur la Cohomologie des Schémas, North-Holland, Amsterdam, pp. 359–386
[12] On the motive of an algebraic surface, J. Reine Angew. Math., Volume 409 (1990), pp. 190-204
[13] On a conjectural filtration on the Chow groups of an algebraic variety I and II, Indag. Math., Volume 2 (1993), pp. 177-188 (189–201)
[14] Toroidal Compactification of Siegel Spaces, Lecture Notes in Math., 812, Springer-Verlag, 1980
[15] Mixed Hodge modules, Publ. RIMS, Kyoto Univ., Volume 26 (1990), pp. 221-333
[16] Motives for modular forms, Invent. Math., Volume 100 (1990), pp. 419-430
Cited by Sources:
Comments - Policy