ALGEBRAIC CYCLES ON COMPACT QUATERNIONIC SHIMURA FOURFOLDS AND POLES OF L-FUNCTIONS
Glasgow mathematical journal, Tome 53 (2011) no. 2, pp. 359-367

Voir la notice de l'article provenant de la source Cambridge University Press

In this article we prove Tate conjecture for a large class of compact quaternionic Shimura fourfolds.
DOI : 10.1017/S0017089510000789
Mots-clés : 11F41, 11F80, 11R42, 11R80, 14C25
VIRDOL, CRISTIAN. ALGEBRAIC CYCLES ON COMPACT QUATERNIONIC SHIMURA FOURFOLDS AND POLES OF L-FUNCTIONS. Glasgow mathematical journal, Tome 53 (2011) no. 2, pp. 359-367. doi: 10.1017/S0017089510000789
@article{10_1017_S0017089510000789,
     author = {VIRDOL, CRISTIAN},
     title = {ALGEBRAIC {CYCLES} {ON} {COMPACT} {QUATERNIONIC} {SHIMURA} {FOURFOLDS} {AND} {POLES} {OF} {L-FUNCTIONS}},
     journal = {Glasgow mathematical journal},
     pages = {359--367},
     year = {2011},
     volume = {53},
     number = {2},
     doi = {10.1017/S0017089510000789},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000789/}
}
TY  - JOUR
AU  - VIRDOL, CRISTIAN
TI  - ALGEBRAIC CYCLES ON COMPACT QUATERNIONIC SHIMURA FOURFOLDS AND POLES OF L-FUNCTIONS
JO  - Glasgow mathematical journal
PY  - 2011
SP  - 359
EP  - 367
VL  - 53
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000789/
DO  - 10.1017/S0017089510000789
ID  - 10_1017_S0017089510000789
ER  - 
%0 Journal Article
%A VIRDOL, CRISTIAN
%T ALGEBRAIC CYCLES ON COMPACT QUATERNIONIC SHIMURA FOURFOLDS AND POLES OF L-FUNCTIONS
%J Glasgow mathematical journal
%D 2011
%P 359-367
%V 53
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000789/
%R 10.1017/S0017089510000789
%F 10_1017_S0017089510000789

[1] 1.Blasius, D., Hilbert modular forms and the Ramanujan conjecture, in Noncommutative geometry and number theory (Aspects Math. vol. E37) (Vieweg, Wiesbaden, 2006) 35–56. Google Scholar | DOI

[2] 2.Carayol, H., Sur la mauvaise réduction des courbes de Shimura, Compositio Mathematica 59 (2) (1986), 151–230. Google Scholar

[3] 3.Flicker, Y. Z. and Hakim, J. L., Quaternionic distinguished representations, Am. J. Math. 116 (3) (June 1994), 683–736. Google Scholar | DOI

[4] 4.Harder, G., Langlands, R. P. and Rapoport, M., Algebraische Zycklen auf Hilbert–Blumenthal–Flächen, J. Reine Angew. Math. 366 (1986), 53–120. Google Scholar

[5] 5.Jacquet, H. and Gelbart, S., A relation between automorphic representations of GL(2) and GL(3), Ann. Sci. École Norm. Sup. 11 (1979), 471–542. Google Scholar

[6] 6.Jacquet, H. and Lai, K., A relative trace formula, Compositio Math. 54 (1985), 243–310. Google Scholar

[7] 7.Jacquet, H., Piatetski-Shapiro, I. I. and Shalika, J. A., Rankin–Selberg convolutions, Am. J. Math. 105 (2) (1983), 367–464. Google Scholar | DOI

[8] 8.Klingenberg, C., Die Tate-Vermutungen für Hilbert–Blumenthal–Flächen, Invent. Math. 89 (1987), 291–317. Google Scholar | DOI

[9] 9.Lai, K. F., Algebraic cycles on compact Shimura surface, Math. Z. 189 (1985), 593–602. Google Scholar | DOI

[10] 10.Langlands, R. P., Base change for GL(2) (Ann. Math. Studies vol. 96) (Princeton University Press, Princeton, NJ, 1980). Google Scholar

[11] 11.Murty, V. K. and Ramakrishnan, D., Period relations and the Tate conjecture for Hilbert modular surfaces, Invent. Math. 89 (1987), 319–345. Google Scholar | DOI

[12] 12.Ramakrishnan, D., Algebraic cycles on Hilbert modular fourfolds and poles of L-functions, in Proceedings of the International Conference on Algebraic Groups and Arithmetic (2005), 271–274. Google Scholar

[13] 13.Ramakrishnan, D., Modular curves, modular surfaces and modular fourfolds, in Algebraic cycles and motives, Volume 1, 278–292, dedicated to Jacob Murre, Cambridge University Press, London Math. Soc. Lecture Notes 343 (2007). Google Scholar | DOI

[14] 14.Ramakrishnan, D., Modularity of solvable Artin representations of GO(4)-type, Int. Math. Res. Not. (1) (2002), 1–54. Google Scholar

[15] 15.Rogawski, J. D. and Tunnell, J. B., On Artin L-functions associated to Hilbert modular forms of weight one, Invent. Math. 74 (1983), 1–43. Google Scholar | DOI

[16] 16.Tate, J., Algebraic cycles and poles of zeta functions, in Arithmetical algebraic geometry (Schilling, O. D. G., Editor) (Harper and Row, New York, 1966). Google Scholar

[17] 17.Taylor, R., On Galois representations associated to Hilbert modular forms, Invent. Math. 98 (1989), 265–280. Google Scholar | DOI

Cité par Sources :