References
[BL] Brylinski, J.-L., Labesse, J.-P.: Cohomologie d'intersection et fonctionsL de certaines variétés de Shimura. Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser.17, 361–412 (1984)
[C] Casselman, W.: The Hasse-Weil Zeta function of some moduli varieties of dimension greater than one. Proc. Symp. Pure Math.33, (part 2) 141–163 (1979)
[D1] Deligne, P.: Travaux de Shimura. Sém. Bourbaki, 23e annee, no.389 (1970/71)
[D2] Deligne, P.: Variétés de Shimura: Interprétation modulaire et techniques de construction de modèles canoniques. Proc. Symp. Pure Math.33, (part 2) 247–289 (1979)
[D3] Deligne, P.: Formes modulaires et representations deGL(2.). In: Modular functions of one variable II, pp. 55–105 Lect. Notes Math., vol. 349. Berlin-Heidelberg-New York: Springer 1973
[D4] Deligne, P.: Périodes d'intégrales et valeurs de fonctionsL. Proc. Symp. Pure Math.33, (part 2) 313–346 (1979)
[DMOS] Deligne, P., Milne, J.S., Ogus, A., Shih, K.-Y.: Hodge cycles. In: Motives and Shimura varieties. Lect. Notes Math., vol. 900. Berlin-Heidelberg-New York: Springer 1982
[GH] Griffiths, P., Harris, J.: Principles of algebraic geometry. New York: John Wiley & Sons 1978
[HLR] Harder, G., Langlands, R.P., Rapoport, M.: Algebraische Zyklen auf Hilbert-Blumenthal-Flächen. J. Reine Angew. Math. (Crelles Journal)366, 53–120 (1986)
[Hd1] Hida, H.: On the abelian varieties with complex multiplication as factors of the abelian varieties attached to Hilbert modular forms. Jap. J. Math., New Ser.5, 157–208 (1979)
[Hd2] Hida, H.: On abelian varieties with complex multiplication as factors of the Jacobian of Shimura curves. Am. J. Math.103, (4), 727–776 (1981)
[H] Hirzebruch, F.: Hilbert modular surfaces. L'Ens. Math.71 (1973)
[HZ] Hirzebruch, F., Zagier, D.: Intersection numbers of curves on Hilbert modular surfaces and modular forms of nebentypus. Invent. math.36, 57–113 (1976)
[JL] Jacquet, H., Langlands, R.P.: Automorphic forms onGL(2). Lect. Notes. Math., vol. 114. Berlin-Heidelberg-New York: Springer 1970
[K] Klingenberg, C.: Die Tate-Vermutungen für Hilbert-Blumenthal-Flächen. (Appearing inthis issue of) Invent. math.89, 291–317 (1987)
[LL] Labesse, J.-P., Langlands, R.P.:L-indistinguishability forSL(2). Can. J. Math.4, 726–785 (1979)
[L] Lai, K.: Algebraic cycles on compact Shimura surfaces. Math. Z.189, 593–602 (1985)
[Mo] Momose, F.: On thel-adic representations attached to modular forms. J. Fac. Sci., Univ. Tokyo, Sect. IA28, (no. 1) 89–109 (1981)
[MR] Murty, V.K., Ramakrishnan, D.: Algebraic cycles on products of Shimura and Fermat curves. Pre-print
[Od1] Oda, T.: Periods of Hilbert modular surfaces. Progress in Math., vol. 19. Boston: Birkhäuser 1982
[Od2] Oda, T.: Hodge structures of Shimura varieties attached to the unit groups of Quaternion algebras. In: Galois groups and their representations. Adv. Stud. Pure Math.2, 15–36 (1983)
[R1] Ramakrishnan, D.: Arithmetic of Hilbert-Blumenthal surfaces. Proceedings of the CMS conf. on Number Theory, to appear (AMS publication)
[R2] Ramakrishnan, D.: Valeura de fonctionsL des surfaces d'Hilbert-Blumenthal ens=1. C.R. Acad. Sc. Paris, Ser. I18, 809–812 (1985)
[Ri] Ribet, K.: Twists of modular forms and endomorphisms of abelian varieties. Math. Ann.253, (no. 1) 43–62 (1980)
[Sh1] Shimura, G.: On elliptic curves with complex multiplication as factors of the Jacobians of the modular function fields. Nagoya Math. J.43, 199–208 (1971)
[Sh2] Shimura, G.: On the factors of the Jacobian variety of a modular function field. J. Math. Soc. Japan25, 523–544 (1973)
[ShT] Shimura, G., Taniyama, Y.: Complex multiplication of abelian varieties and its applications to number theory. Publ. Math. Soc. Japan6 (1961)
[T] Tate, J.: Algebraic cycles and poles of Zeta functions. In: Schilling, O.F.G. (ed.), Arithmetical algebraic geometry. New York: Harper & Row, 1966
Author information
Authors and Affiliations
Additional information
Supported by NSERC grant U0373
Partially supported by a grant from the National Science Foundation
Rights and permissions
About this article
Cite this article
Murty, V.K., Ramakrishnan, D. Period relations and the Tate conjecture for Hilbert modular surfaces. Invent Math 89, 319–345 (1987). https://doi.org/10.1007/BF01389081
Issue Date:
DOI: https://doi.org/10.1007/BF01389081