On the cuspidal cohomology of S-arithmetic subgroups of reductive groups over number fields
Compositio Mathematica, Tome 102 (1996) no. 1, pp. 1-40.
@article{CM_1996__102_1_1_0,
     author = {Borel, A. and Labesse, J.-P. and Schwermer, J.},
     title = {On the cuspidal cohomology of $S$-arithmetic subgroups of reductive groups over number fields},
     journal = {Compositio Mathematica},
     pages = {1--40},
     publisher = {Kluwer Academic Publishers},
     volume = {102},
     number = {1},
     year = {1996},
     mrnumber = {1394519},
     zbl = {0853.11044},
     language = {en},
     url = {http://archive.numdam.org/item/CM_1996__102_1_1_0/}
}
TY  - JOUR
AU  - Borel, A.
AU  - Labesse, J.-P.
AU  - Schwermer, J.
TI  - On the cuspidal cohomology of $S$-arithmetic subgroups of reductive groups over number fields
JO  - Compositio Mathematica
PY  - 1996
SP  - 1
EP  - 40
VL  - 102
IS  - 1
PB  - Kluwer Academic Publishers
UR  - http://archive.numdam.org/item/CM_1996__102_1_1_0/
LA  - en
ID  - CM_1996__102_1_1_0
ER  - 
%0 Journal Article
%A Borel, A.
%A Labesse, J.-P.
%A Schwermer, J.
%T On the cuspidal cohomology of $S$-arithmetic subgroups of reductive groups over number fields
%J Compositio Mathematica
%D 1996
%P 1-40
%V 102
%N 1
%I Kluwer Academic Publishers
%U http://archive.numdam.org/item/CM_1996__102_1_1_0/
%G en
%F CM_1996__102_1_1_0
Borel, A.; Labesse, J.-P.; Schwermer, J. On the cuspidal cohomology of $S$-arithmetic subgroups of reductive groups over number fields. Compositio Mathematica, Tome 102 (1996) no. 1, pp. 1-40. http://archive.numdam.org/item/CM_1996__102_1_1_0/

[A1] Arthur, J.: A trace formula for reductive groups I: Terms associated to classes in G(Q), Duke Math. J. 45 (1978) 911-952. | MR | Zbl

[A2] Arthur, J.: A trace formula for reductive groups II: Applications of a truncation operator, Compos. Math. 40 (1980) 87-121. | EuDML | Numdam | MR | Zbl

[A3] Arthur, J.: A Paley-Wienertheorem for real reductive groups, Acta Mathematica 150 (1983) 1-89. | MR | Zbl

[A4] Arthur, J.: The invariant trace formula. I. Local theory, J. Amer. Math. Soc. 1 (1988) 323-383. | MR | Zbl

[A5] Arthur, J.: The invariant trace formula. II. Global theory, J. Amer. Math. Soc. 1 (1988) 501-554. | MR | Zbl

[AC] Arthur, J. and Clozel, L.: Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula, Annals of Math. Studies 120, Princeton Univ. Press, 1989. | MR | Zbl

[BDK] Bernstein, J., Deligne, P. and Kazhdan, D.: Trace Paley-Wiener theorem for reductive p-adic groups, Journal d'Analyse Mathématique 47 (1986) 180-192. | MR | Zbl

[BFG] Blasius, D., Franke, J. and Grunewald, F.: Cohomology of S-arithmetic groups in the number field case, Invent. Math. 116 (1994) 75-93. | EuDML | MR | Zbl

[B1] Borel, A.: Some finiteness properties of adele groups over number fields, Publ. Math. I.H.E.S. 16 (1963) 5-30. | EuDML | Numdam | MR | Zbl

[B2] Borel, A.: Introduction aux Groupes Arithmétiques, Hermann, Paris, 1969. | MR | Zbl

[B3] Borel, A.: Admissible representations of a semisimple group over a local field with vectors fixed under an Iwahori subgroup, Invent. Math. 35 (1976) 233-259. | MR | Zbl

[B4] Borel, A.: Stable real cohomology of arithmetic groups II. Manifolds and Lie groups, J. Hano et al. (eds.), Progress in Math. 14, 21-55, Birkhäuser, Boston, Basel, Stuttgart, 1981. | MR | Zbl

[B5] Borel, A.: Regularization theorems in Lie algebra cohomology. Applications, Duke Math. J. 50 (1983) 605-623. | MR | Zbl

[BC] Borel, A. and Casselman, W.: L2-Cohomology of locally symmetric manifolds of finite volume, Duke Math. J. 50 (1983) 625-647. | MR | Zbl

[BG] Borel, A. and Garland, H.: Laplacian and discrete spectrum of an arithmetic group, Amer. J. Math. 105 (1983) 309-335. | MR | Zbl

[BJ] Borel, A. and Jacquet, H.: Automorphic Forms and Automorphic Representations in Automorphic Forms, Representations and L-functions Proc. of Symp. in Pure Math. 33(1), 189-202, A.M.S., Providence, 1979. | MR | Zbl

[BS] Borel, A. and Serre, J.-P.: Cohomologie d'immeubles et de groupes S-arithmétiques, Topology 15 (1976) 211-232. | MR | Zbl

[BT] Borel, A. and Tits J.: Homomorphismes 'abstraits' de groupes algébriques simples; Annals of Math. 97 (1973) 499-571. | MR | Zbl

[BW] Borel, A. and Wallach, N.: Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups, Annals of Math. Studies 94, Princeton Univ. Press, Princeton, 1980. | MR | Zbl

[Bou] Bouaziz, A.: Sur les caractères des groupes de Lie réductifs non connexes, Journal of Funct. Anal. 70 (1987) 1-79. | MR | Zbl

[Ca1] Casselman, W.: A new non-unitary argument for p-adic representations, J. Fac. Sci. Univ. Tokyo 28 (1982) 907-928. | Zbl

[Ca2] Casselman, W.: Introduction to the Schwartz space of Γ\G, Can. J. Math XLI (1989) 285-320. | Zbl

[Cl1] Clozel, L.: Characters of non-connectedp-adic groups, Canad. J. Math. 39 (1987) 149-167. | MR | Zbl

[Cl2] Clozel, L.: Représentations galoisiennes associées aux représentations automorphes autoduales de GL(n), Publ. Math. IHES 73 (1991) 97-145. | Numdam | MR | Zbl

[Cl3] Clozel, L.: On the cohomology of Kottwitz's arithmetic varieties, Duke Math. J. 72 (1993) 757-795. | MR | Zbl

[CD] Clozel, L. and Delorme, P.: Le théorème de Paley-Wiener invariant pour les groupes de Lie réductifs II, Ann. Sci. Ec. Norm. Sup. 4e serie 23 (1990) 193-228. | Numdam | MR | Zbl

[D] Delorme, P.: Théorème de Paley-Wiener invariant tordu pour le changement de base C/R, Compositio Math. 80 (1991) 197-228. | Numdam | MR | Zbl

[DM] Dixmier, J. and Malliavin, P.: Factorisations de fonctions et de vecteurs indéfiniment différentiables, Bull. Sci. Math. 102 (1978) 307-330. | MR | Zbl

[F] Franke, J.: Harmonic analysis in weighted L2-spaces. In preparation.

[HC] Harish-Chandra Automorphic Forms on Semisimple Lie Groups, Lect. Notes in Math. 62, Springer-Verlag, Berlin, Heidelberg, New York, 1968. | MR | Zbl

[Hel] Helgason, S.: Differential Geometry and Symmetric Spaces, Pure and Applied Math. 12, Academic Press, 1962. | MR | Zbl

[J] Johnson, J.F.: Stable base change C/R of certain derived functor modules, Math. Annalen 287 (1990) 467-493. | MR | Zbl

[Ko] Kottwitz, R.E.: Tamagawa numbers, Annals of Math. 127 (1988) 629-646. | MR | Zbl

[Lab] Labesse, J.-P.: Pseudo-coefficients très cuspidaux et K-theorie, Math. Ann. 291 (1991) 607-616. | MR | Zbl

[LS] Labesse, J.-P. and Schwermer, J.: On liftings and cusp cohomology of arithmetic groups, Invent. Math. 83 (1986) 383-401. | MR | Zbl

[Lan1] Langlands, R.P.: On the Functional Equations Satisfied by Eisenstein Series, Lect. Notes in Math. 544, Springer, Berlin, Heidelberg, New York, 1976. | MR | Zbl

[Lan2] Langlands, R.P.: Letter to A. Borel dated October 25, 1972.

[Lau] Laumon, G.: Cohomology with compact support of Drinfeld modular varieties. Part I. Publication de l'Université de Paris-Sud, 1991.

[MW] Mœglin, C. and Waldspurger, J-L.: Déeompositionspectraleet séries d'Eisenstein, Progress in Math. 113, Birkhäuser, Boston, Basel, Berlin, 1994. | Zbl

[Mü] Müller, W.: The trace class conjecture in the theory of automorphic forms, Annals of Math. 130 (1989) 473-529. | MR | Zbl

[OW] Osborne, M.S. and Warner, G.: The Selberg trace formula II: Partition, reduction, truncation, Pacific J. Math. 106 (1983) 307-496. | MR | Zbl

[Ro] Rogawski, J.D.: Trace Paley Wiener theorem in the twisted case, Transactions AMS 309 (1988) 215-229. | MR | Zbl

[RS1] Rohlfs, J. and Speh, B.: Automorphic representations and Lefschetz numbers, Ann. Sci. Ec. Norm. Sup. 4e série 22 (1989) 473-499. | Numdam | MR | Zbl

[RS2] Rohlfs, J. and Speh, B.: Lefschetz numbers and twisted stabilized orbital integrals, Math. Ann. 296 (1993) 191-214. | MR | Zbl

[RS3] Rohlfs, J. and Speh, B.: On the cuspidal cohomology of arithmetic groups and cyclic base change, Math. Nach. 158 (1992) 99-108. | MR | Zbl

[Sch] Schwermer, J.: Cohomology of arithmetic groups, automorphic forms and L-functions, Cohomology of Arithmetic Groups and Automorphic forms, Lect. Notes in Math. 1447, Springer, Berlin, Heidelberg, New York, 1990. | MR | Zbl

[Sil] Silberger, A.: Isogeny restriction of irreducible admissible representations are finite direct sums of irreducible admissible representations, Proc. AMS 73 (1979) 263-264. | MR | Zbl

[T] Tits, J.: Algebraic and abstract simple groups, Annals of Math. 80 (1964) 313-329. | MR | Zbl

[VZ] Vogan, D. and Zuckerman, G.J.: Unitary representations with non-zero cohomology, Compositio Math. 53 (1984) 51-90. | Numdam | MR | Zbl

[W] Wallach, N.: On the constant term of a square-integrable automorphic form, Operator algebras and group representations II, Monographs and Studies in Math. 17 (1984) 227-237, Pitman, London. | MR | Zbl