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Algebraic cycles on a product of two Hilbert modular surfaces


Author: Cristian Virdol
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
Published electronically: February 17, 2010
MathSciNet review: 2601605
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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.


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  • [D] P. Deligne, Travaux de Shimura, Sém. Bourbaki Féb. 71, Exposé 389, Lectures Notes in Math. vol. 244. Berlin-Heidelberg-New York; Springer, 1971. MR 0498581 (58:16675)
  • [FH] Y. Z. Flicker, J. L. Hakim, Quaternionic Distinguished Representations, American J. of Math., Vol. 116, No. 3. (Jun., 1994), 683-736. MR 1277452 (95i:22028)
  • [HLR] G. Harder, R. P. Langlands, M. Rapoport, Algebraische Zycklen auf Hilbert-Blumenthal-Flächen, J. Reine Angew. Math. 366, 53-120 (1986). MR 833013 (87k:11066)
  • [G] G. van der Geer, Hilbert modular surfaces, Springer-Verlag, 1988. MR 930101 (89c:11073)
  • [GJ] S. Gelbart, H. Jacquet, A relation between automorphic representations of $ GL(2)$ and $ GL(3)$, Ann. Sci. École Norm. Sup. 11(1979),471-542. MR 533066 (81e:10025)
  • [JPSS] H. Jacquet, I. I. Piatetski-Shapiro, J. A. Shalika, Rankin-Selberg convolutions, American J. of Math., 105, nr. 2 (1983), 367-464. MR 701565 (85g:11044)
  • [K] C. Klingenberg, Die Tate-Vermutungen für Hilbert-Blumenthal-Flächen, Invent. Math. 89, 291-317(1987). MR 894381 (88m:11042)
  • [L] R. P. Langlands, Base change for GL(2), Ann. of Mathematics Studies 96, Princeton University Press, 1980. MR 574808 (82a:10032)
  • [LA] K. F. Lai, Algebraic cycles on compact Shimura surface, Math. Z. 189, 593-602 (1985). MR 786286 (87a:11057)
  • [MP] V. K. Murty, D. Prasad, Tate cycles on a product of two Hilbert modular surfaces, J. Number Theory 80(1)(2000) 25-43. MR 1735646 (2000m:14028)
  • [MR] V. K. Murty, D. Ramakrishnan, Period relations and the Tate conjecture for Hilbert modular surfaces, Invent. Math. 89, 319-345(1987). MR 894382 (89a:11064)
  • [R] D. Ramakrishnan, Modularity of solvable Artin representations of $ GO(4)$-type, IMRN 2002, No. 1, 1-54. MR 1874921 (2003b:11049)
  • [RT] J. D. Rogawski, J. B. Tunnell, On Artin L-functions associated to Hilbert modular forms of weight one, Invent. Math. 74, 1983, 1-43. MR 722724 (85i:11044)
  • [T] R. Taylor, On Galois representations associated to Hilbert modular forms, Invent. Math. 98, 1989, 265-280. MR 1016264 (90m:11176)
  • [TA] J. Tate, Algebraic cycles and poles of zeta functions, In: Schilling, O.D.G. (ed.), Arithmetical algebraic geometry, New York: Harper and Row, 1966. MR 0225778 (37:1371)

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Additional Information

Cristian Virdol
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027

DOI: https://doi.org/10.1090/S0002-9947-10-05116-0
Received by editor(s): July 17, 2008
Published electronically: February 17, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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