Advertisement

Inventiones mathematicae

, Volume 89, Issue 1, pp 37–118 | Cite as

Eisenstein cohomology of arithmetic groups. The case GL2

  • G. Harder
Article

Keywords

Arithmetic Group Eisenstein Cohomology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Bo 1] Borel, A.: Stable real cohomology of arithmetic groups. Ann. Sci. Ec. Norm. Super. (4)7: 235–272 (1974)Google Scholar
  2. [Bo 2] Borel, A.: Stable real cohomology of arithmetic groups II. Prog. Math. Boston14: 21–55 (1981)Google Scholar
  3. [Bo 3] Borel, A.: Cohomologie de sous-groupes discrets et représentations de groupes semi-simples. Astérisque32–33: 73–112 (1976)Google Scholar
  4. [B-S] Borel, A., Serre, J-P.: Corners and arithmetic groups Comment. Math. Helv.48: 436–491 (1973)Google Scholar
  5. [B-W] Borel, A., Wallach, N.: Continuous cohomology, discrete subgroups, and representations of reductive groups. Ann. Math. Stud., Princeton University Press, 1980Google Scholar
  6. [Ch] Chevalley, C.: Deux théorèmes d'arithmétique. J. Math. Soc. Japan, c, 1951, pp. 33–44Google Scholar
  7. [D] Deligne, P.: Valeurs de fonctionsL et périodes d'intégrales. Proc. Symp. Pure Math.33 (part. 2): 313–346 (1979)Google Scholar
  8. [DB] Don Blasius: On the critical values of HeckeL-series. Ann. Math.124:23–63 (1986)Google Scholar
  9. [Do] Delorme, P.: Letter to A. BorelGoogle Scholar
  10. [Du] Duflo, M.: Représentations irréducibles des groupes semi-simples complexes. Analyse Harmonique sur les groupes de Lie, Séminaire Nancy-Straßbourg 1973–75, LN 497, 1975, pp. 26–88Google Scholar
  11. [En] Enright, T.: Relative Lie algebra cohomology and unitary representations of complex Lie groups. Duke Math. J.46: 513–525 (1979)Google Scholar
  12. [Fl] Flath, D.: Decomposition of representations into tensor products. Proc. Symp. Pure Math.33: I, 179–183 (1979)Google Scholar
  13. [G-J] Gelbart, S., Jacquet, H.: Forms of GL(2) from the analytic point of view. Proc. Symp. Pure Math.33 (I): 213–251 (1979)Google Scholar
  14. [Go] Godement, R.: Notes on Jacquet-Langlands' Theory. The Institute for Advanced Study, 1970Google Scholar
  15. [Gr] Grothendieck, A.: Sur quelques points d'algèbre homologique. Tohoku Math. J.9: 119–221 (1957)Google Scholar
  16. [Ha 1] Harder, G.: Cohomology of SL2(0), Lie groups and their representations. In: Gelfand, I.M. (ed.). Proc. of the Summer School on Group Repres. London: A. Hilger, 1975, pp. 139–150Google Scholar
  17. [Ha 2] Harder, G.: On the cohomology of discrete arithmetically defined groups. Proc. of the Int. Colloquium on Discrete Subgroups and Applications to Moduli, Bombay, 1973; Oxford University Press, 1975, pp. 129–160Google Scholar
  18. [Ha 3] Harder, G.: Period Integrals of Cohomology Classes which are Represented by Eisenstein Series. Proc. Bombay Colloquium 1979, Berlin Heidelberg New York: Springer 1981, pp. 41–115Google Scholar
  19. [Ha 4] Harder, G.: Period integrals of Eisenstein cohomology classes and special values of someL-functions, Number theory related to Fermat's last theorem. In: Koblitz, Neal (ed.) Progr. Math.26, pp. 103–142 (1982)Google Scholar
  20. [Ha 5] Harder, G.: General aspects in the theory of modular symbols. In: Bertin, M.-J. (ed.) Séminaire de Théorie des Nombres, Paris 1981–82. Progr. Math. vol.38: 73–88 (1983)Google Scholar
  21. [H-S] Harder, G., Schappacher, N.: Special values of HeckeL-functions and abelian integrals. Lect. Notes Math., Berlin Heidelberg New York: Springer 1111, 1985, pp. 17–49Google Scholar
  22. [HC] Harish-Chandra: Automorphic forms on semisimple Lie groups. Lect. Notes Math., Berlin Heidelberg New York: Springer, 62, 1968Google Scholar
  23. [J-L] Jacquet, H., Langlands, R.: Automorphic forms on GL(2). Lect. Notes Math.114 (1970)Google Scholar
  24. [Kn] Kneser, M.: Schwache Approximation in algebraischen Gruppen. Colloque sur la théorie des groupes algébriques, CBRM, Bruxelles, 1962Google Scholar
  25. [Ko] Kostant, B.: Lie algebra cohomology and the generalized Borel-Weil theorem. Ann. Math.74: 329–387 (1961)Google Scholar
  26. [Lg] Lang, S.: Algebraic Number Theory. Reading, MA, Addison Wesley Publ. Company, 1970Google Scholar
  27. [La] Langlands, R.: On the functional equation satisfied by Eisenstein series. Lect. Notes Math. Berlin Heidelberg New York: Springer, 544, 1976Google Scholar
  28. [M-M] Matsushima, Y., Murakami, S.: On vector bundle valued harmonic forms and automorphic forms on symmetric Riemannian manifolds. Ann. Math.78: 365–416 (1963)Google Scholar
  29. [Se 1] Serre, J.-P.: Abelianl-adic representations and elliptic curves. New York Amsterdam: Benjamin 1968Google Scholar
  30. [Se 2] Serre, J.-P.: Le problème des groupes de congruence pour SL2. Ann. Math.92: 489–527 (1970)Google Scholar
  31. [Sie] Siegel, C.L.: Über die Fourierschen Koeffizienten von Modulformen. Gött. Nachr.3: 15–56 (1970) (=Ges. Abh., IV, 18–139)Google Scholar
  32. [Schw] Schwermer, J.: Konomologie arithmetisch definierter Gruppen und Eisensteinreihen. Lect. Notes Math., Berlin Heidelberg New York: Springer, 988, 1983Google Scholar
  33. [Sp] Speh, B.: Unitary representations of GL(n,R) with non-trivial (g, K)-cohomology. Invent. Math.71: 433–465 (1983)Google Scholar
  34. [vE] van Est: A generalization of the Cartan-Leray spectral sequence II. Indagationes Math.20: (series A) 406–413 (1958)Google Scholar
  35. [Vo 1] Vogan, D.: Representations of real reductive Lie groups. Prog. Math., Boston15 (1981)Google Scholar
  36. [Vo 2] Vogan, D.: Unitarizability of certain series of representations. Ann. Math.120: 141–187 (1984)Google Scholar
  37. [V-Z] Vogan, D., Zuckerman, G.: Unitary representations with non-zero cohomology. Compos. Math.53: 51–90 (1984)Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • G. Harder
    • 1
  1. 1.Mathematisches InstitutUniversität BonnBonnFederal Republic of Germany

Personalised recommendations