Comptes Rendus
Chow–Künneth projectors for modular varieties
[Projecteurs de Chow–Künneth pour des variétés modulaires]
Comptes Rendus. Mathématique, Volume 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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02506-2

B.Brent Gordon 1 ; Masaki Hanamura 2 ; Jacob P. Murre 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
@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},
}
TY  - JOUR
AU  - B.Brent Gordon
AU  - Masaki Hanamura
AU  - Jacob P. Murre
TI  - Chow–Künneth projectors for modular varieties
JO  - Comptes Rendus. Mathématique
PY  - 2002
SP  - 745
EP  - 750
VL  - 335
IS  - 9
PB  - Elsevier
DO  - 10.1016/S1631-073X(02)02506-2
LA  - en
ID  - CRMATH_2002__335_9_745_0
ER  - 
%0 Journal Article
%A B.Brent Gordon
%A Masaki Hanamura
%A Jacob P. Murre
%T Chow–Künneth projectors for modular varieties
%J Comptes Rendus. Mathématique
%D 2002
%P 745-750
%V 335
%N 9
%I Elsevier
%R 10.1016/S1631-073X(02)02506-2
%G en
%F CRMATH_2002__335_9_745_0
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] A. Ash; D. Mumford; M. Rapoport; Y. Tai Smooth Compactification of Locally Symmetric Varieties, Math. Sci. Press, 1975

[2] A. Beilinson; J. Bernstein; P. Deligne Faisceaux Pervers, Analyse et topologie sur les espaces singuliers, Astérisque, Volume 100 (1982), pp. 7-171

[3] A. Borel 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] C. Deninger; J.P. Murre Motivic decomposition of abelian schemes and the Fourier transform, J. Reine Angew. Math., Volume 422 (1991), pp. 201-219

[6] W. Fulton Intersection Theory, Springer, 1984

[7] M. Goresky; R. MacPherson Intersection homology II, Inv. Math., Volume 71 (1983), pp. 77-129

[8] B. Gordon; J.P. Murre Chow motives of elliptic modular surfaces and threefolds, Report W 96-16, Math. Institut, Univ. of Leiden, 1996

[9] B. Gordon; J.P. Murre Chow motives of elliptic modular threefolds, J. Reine Angew. Math., Volume 514 (1999), pp. 145-164

[10] A. Grothendieck 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] J.P. Murre On the motive of an algebraic surface, J. Reine Angew. Math., Volume 409 (1990), pp. 190-204

[13] J.P. Murre 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] Y. Namikawa Toroidal Compactification of Siegel Spaces, Lecture Notes in Math., 812, Springer-Verlag, 1980

[15] M. Saito Mixed Hodge modules, Publ. RIMS, Kyoto Univ., Volume 26 (1990), pp. 221-333

[16] A.J. Scholl Motives for modular forms, Invent. Math., Volume 100 (1990), pp. 419-430

Cité par Sources :

Commentaires - Politique