Skip to main content
Log in

Die Tate-Vermutungen für Hilbert-Blumenthal-Flächen

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literatur

  1. Baily, W., Borel, A.: Compactification of arithmetic quotients of bounded symmetric domains. Ann. Math., II. Ser.84, 442–528 (1966)

    Google Scholar 

  2. Borel, A., Wallach, N.: Continuous cohomology, discrete subgroups and representations of reductive groups. PUP Ann. Math. Stud.94. Princeton 1980

  3. Deligne, P.: Varietes de Shimura. In: Automorphic Forms, Representations and L-Functions. Proc. Symp. Pure Math.33, (Corvallis). II, 247–290 (1979)

  4. Deligne, P.: Valeurs de fonctionsL et periodes d'integrales. In: Automorphic Forms, Representations andL-Functions. Proc. Symp. Pure Math.33, (Corvallis). Il, 313–346 (1979)

  5. Deligne, P.: Travaux de Shimura. Seminaire Bourbaki, Exp.389, 123–165 (1971)

    Google Scholar 

  6. Deligne, P., Milne, J., Ogus, A., Shih, K.: Hodge cycles, Shimura varieties and motives. Lect. Notes Math., vol. 900. Berlin-Heidelberg-New York: Springer 1979 (Wir beziehen uns nur auf den ersten Artikel von P. Deligne: Hodge cycles on abelian varieties)

    Google Scholar 

  7. Doi, K., Naganuma, H.: On the functional equations of certain Dirichlet series. Invent. Math.9, 1–14 (1969)

    Google Scholar 

  8. Faltings, G.: Endlichkeitssätze für abelsche Varietäten über Zahlkörpern. Invent. Math.73, 349–366 (1983)

    Google Scholar 

  9. Faltings, G., Wüstholz, G.: Rational points. Braunschweig: Viehweg 1984

    Google Scholar 

  10. Gelbart, S.: Automorphic forms on adele groups. PUP Ann. Math. Stud.83. Princeton 1975

  11. Griffiths, P., Harris, J.: Principles of algebraic geometry. New York: John Wiley 1978

    Google Scholar 

  12. Gelbart, S., Knapp, A.:L-indistinguishability andR-groups for the special linear group. Adv. Math.43, 101–121 (1982)

    Google Scholar 

  13. Hammond, W.F., hirzebruch, F.:L-series, modular imbeddings and signatures. Math. Ann.204, 263–270 (1972)

    Google Scholar 

  14. Harder, G.: General aspects in the theory of modular symbols. Semin. Theor. Nombres, Univ. Paris, 73–88 (1981–82)

  15. Harder, G.: The cohomology of\(SL_2 (\mathcal{O})\). In: Gelfand, A. (ed.), Lie Groups and their Representations, pp. 139–150 London: Hilger 1975

    Google Scholar 

  16. Harder, G., Langlands, R.P., Rapoport, M.: Algebraische Zyklen auf Hilbert-Blumenthal-Flächen. J. Reine Angew. Math.366, 53–120 (1986)

    Google Scholar 

  17. Hirzebruch, F., Zagier, D.: Intersection numbers of curves on Hilbert modular surfaces. Invent. Math.36, 57–113 (1976)

    Google Scholar 

  18. Jacquet, H., Langlands, R.P.: Automorphic forms onGL(2). Lect. Notes Math., vol. 114. Berlin-Heidelberg-New York: Springer 1970

    Google Scholar 

  19. Koehl, J.: Die Picardzahl der Hilbertschen Modulflächen. Dissertation Bonn (in Vorbereitung)

  20. Labesse, J.:L-indistinguishable representations and the trace formula forSL(2). In: Gelfand, A. (ed.), Lie Groups and their Representations, pp. 331–338. London: Hilger 1975

    Google Scholar 

  21. Labesse, J., Langlands, R.P.:L-indistinguishability forSL(2). Can. J. Math.31, 726–785 (1979)

    Google Scholar 

  22. Lai, K.F.: Algebraic cycles on compact Shimura surface. Math. Z.189, 593–602 (1985)

    Google Scholar 

  23. Langlands, R.P.: Base change forGL(2). PUP Ann. Math. Stud96. Princeton 1980

  24. Murty, V.K., Ramakrishnan, D.: Period relations and the Tate conjecture for Hilbert modular surfaces. Invent. Math.89, 319–345 (1987)

    Google Scholar 

  25. Oda, T.: Periods of Hilbert modular surfaces. PM, vol. 19. Boston: Birkhäuser 1982

    Google Scholar 

  26. Rapoport, M.: Compactification de l'espace de modules de Hilbert-Blumenthal. Compos. Math.36, 255–335 (1978)

    Google Scholar 

  27. Shimura, G.: On canonical models of arithmetic quotients of bounded symmetric domains. Ann. Math.91, 114–222 (1970)

    Google Scholar 

  28. Tate, J.: Algebraic cycles and poles of zetafunctions. Proc. Conf. Purdue Univ. 1963, Shilling, A. (ed.). New York: Harper and Row, 1963

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Klingenberg, C. Die Tate-Vermutungen für Hilbert-Blumenthal-Flächen. Invent Math 89, 291–317 (1987). https://doi.org/10.1007/BF01389080

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01389080

Navigation