Algebraic cycles on a product of two Hilbert modular surfaces
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- by Cristian Virdol PDF
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Abstract:
In this paper we prove the Tate conjecture for a product of two Hilbert modular surfaces for non-CM submotives.References
- Pierre Deligne, Travaux de Shimura, Séminaire Bourbaki, 23ème année (1970/71), Exp. No. 389, Lecture Notes in Math., Vol. 244, Springer, Berlin, 1971, pp. 123–165 (French). MR 0498581
- Yuval Z. Flicker and Jeffrey L. Hakim, Quaternionic distinguished representations, Amer. J. Math. 116 (1994), no. 3, 683–736. MR 1277452, DOI 10.2307/2374997
- G. Harder, R. P. Langlands, and M. Rapoport, Algebraische Zyklen auf Hilbert-Blumenthal-Flächen, J. Reine Angew. Math. 366 (1986), 53–120 (German). MR 833013
- Gerard van der Geer, Hilbert modular surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 16, Springer-Verlag, Berlin, 1988. MR 930101, DOI 10.1007/978-3-642-61553-5
- Stephen Gelbart and Hervé Jacquet, A relation between automorphic representations of $\textrm {GL}(2)$ and $\textrm {GL}(3)$, Ann. Sci. École Norm. Sup. (4) 11 (1978), no. 4, 471–542. MR 533066
- H. Jacquet, I. I. Piatetskii-Shapiro, and J. A. Shalika, Rankin-Selberg convolutions, Amer. J. Math. 105 (1983), no. 2, 367–464. MR 701565, DOI 10.2307/2374264
- Christoph Klingenberg, Die Tate-Vermutungen für Hilbert-Blumenthal-Flächen, Invent. Math. 89 (1987), no. 2, 291–317 (German). MR 894381, DOI 10.1007/BF01389080
- Robert P. Langlands, Base change for $\textrm {GL}(2)$, Annals of Mathematics Studies, No. 96, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1980. MR 574808
- K. F. Lai, Algebraic cycles on compact Shimura surface, Math. Z. 189 (1985), no. 4, 593–602. MR 786286, DOI 10.1007/BF01168162
- V. Kumar Murty and Dipendra Prasad, Tate cycles on a product of two Hilbert modular surfaces, J. Number Theory 80 (2000), no. 1, 25–43. MR 1735646, DOI 10.1006/jnth.1999.2446
- V. Kumar Murty and Dinakar Ramakrishnan, Period relations and the Tate conjecture for Hilbert modular surfaces, Invent. Math. 89 (1987), no. 2, 319–345. MR 894382, DOI 10.1007/BF01389081
- Dinakar Ramakrishnan, Modularity of solvable Artin representations of $\textrm {GO}(4)$-type, Int. Math. Res. Not. 1 (2002), 1–54. MR 1874921, DOI 10.1155/S1073792802000016
- J. D. Rogawski and J. B. Tunnell, On Artin $L$-functions associated to Hilbert modular forms of weight one, Invent. Math. 74 (1983), no. 1, 1–42. MR 722724, DOI 10.1007/BF01388529
- Richard Taylor, On Galois representations associated to Hilbert modular forms, Invent. Math. 98 (1989), no. 2, 265–280. MR 1016264, DOI 10.1007/BF01388853
- John T. Tate, Algebraic cycles and poles of zeta functions, Arithmetical Algebraic Geometry (Proc. Conf. Purdue Univ., 1963) Harper & Row, New York, 1965, pp. 93–110. MR 0225778
Additional Information
- Cristian Virdol
- Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
- MR Author ID: 781239
- Received by editor(s): July 17, 2008
- Published electronically: February 17, 2010
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 362 (2010), 3691-3703
- MSC (2000): Primary 11R42, 11R80
- DOI: https://doi.org/10.1090/S0002-9947-10-05116-0
- MathSciNet review: 2601605