Remote Access Journal of the American Mathematical Society
Green Open Access

Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)

 

 

Intersection numbers of special cycles


Authors: Jürgen Rohlfs and Joachim Schwermer
Journal: J. Amer. Math. Soc. 6 (1993), 755-778
MSC: Primary 11F75; Secondary 55N45
MathSciNet review: 1186963
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] Armand Borel, Introduction aux groupes arithmétiques, Publications de l’Institut de Mathématique de l’Université de Strasbourg, XV. Actualités Scientifiques et Industrielles, No. 1341, Hermann, Paris, 1969 (French). MR 0244260
  • [2] A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces. I, Amer. J. Math. 80 (1958), 458–538. MR 0102800
  • [3] A. Borel and J.-P. Serre, Théorèmes de finitude en cohomologie galoisienne, Comment. Math. Helv. 39 (1964), 111–164 (French). MR 0181643
  • [4] Armand Borel and Jacques Tits, Groupes réductifs, Inst. Hautes Études Sci. Publ. Math. 27 (1965), 55–150 (French). MR 0207712
  • [5] -, Compléments à l'article: `Groupes réductifs', Inst. Hautes Études Sci. Publ. Math. 41 (1972), 253-276.
  • [6] C. Chevalley, Theory of Lie groups, Princeton Univ. Press, Princeton, NJ, 1946.
  • [7] William Fulton, Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 2, Springer-Verlag, Berlin, 1984. MR 732620
  • [8] Werner Greub, Stephen Halperin, and Ray Vanstone, Connections, curvature, and cohomology, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. Volume III: Cohomology of principal bundles and homogeneous spaces; Pure and Applied Mathematics, Vol. 47-III. MR 0400275
  • [9] G. Harder, A Gauss-Bonnet formula for discrete arithmetically defined groups, Ann. Sci. École Norm. Sup. (4) 4 (1971), 409–455. MR 0309145
  • [10] Sigurđur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962. MR 0145455
  • [11] Friedrich Hirzebruch, Automorphe Formen und der Satz von Riemann-Roch, Symposium internacional de topología algebraica International symposium on algebraic topology, Universidad Nacional Autónoma de México and UNESCO, Mexico City, 1958, pp. 129–144 (German). MR 0103280
  • [12] F. Hirzebruch and D. Zagier, Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus, Invent. Math. 36 (1976), 57–113. MR 0453649
  • [13] H. Hopf and H. Samelson, Ein Satz über die Wirkungsräume geschlossener Liescher Gruppen, Comment. Math. Helv. 13 (1941), 240–251 (German). MR 0006546
  • [14] Dale Husemoller, Fibre bundles, 2nd ed., Springer-Verlag, New York-Heidelberg, 1975. Graduate Texts in Mathematics, No. 20. MR 0370578
  • [15] Hervé Jacquet and Stephen Rallis, Symplectic periods, J. Reine Angew. Math. 423 (1992), 175–197. MR 1142486
  • [16] Stephen S. Kudla and John J. Millson, Intersection numbers of cycles on locally symmetric spaces and Fourier coefficients of holomorphic modular forms in several complex variables, Inst. Hautes Études Sci. Publ. Math. 71 (1990), 121–172. MR 1079646
  • [17] Serge Lang, Algebraic number theory, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London-Don Mills, Ont., 1970. MR 0282947
  • [18] Ronnie Lee and Joachim Schwermer, Geometry and arithmetic cycles attached to 𝑆𝐿₃(𝑍). I, Topology 25 (1986), no. 2, 159–174. MR 837619, 10.1016/0040-9383(86)90037-6
  • [19] John J. Millson, Cycles and harmonic forms on locally symmetric spaces, Canad. Math. Bull. 28 (1985), no. 1, 3–38. MR 778258, 10.4153/CMB-1985-001-x
  • [20] -, Geometric construction of homology for arithmetic groups. II, unpublished manuscript, 1981.
  • [21] John J. Millson and M. S. Raghunathan, Geometric construction of cohomology for arithmetic groups. I, Geometry and analysis, Indian Acad. Sci., Bangalore, 1980, pp. 103–123. MR 592256
  • [22] John W. Milnor and James D. Stasheff, Characteristic classes, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1974. Annals of Mathematics Studies, No. 76. MR 0440554
  • [23] H. Minkowski, Über den arithmetischen Begriff der Äquivalenz und über die endlichen Gruppen linearer ganzzahliger Substitutionen, J. Reine Angew. Math. 100 (1887), 449-458.
  • [24] David Mumford, Algebraic geometry. I, Springer-Verlag, Berlin-New York, 1976. Complex projective varieties; Grundlehren der Mathematischen Wissenschaften, No. 221. MR 0453732
  • [25] Daniel Quillen, Elementary proofs of some results of cobordism theory using Steenrod operations, Advances in Math. 7 (1971), 29–56 (1971). MR 0290382
  • [26] J. Rohlfs, Arithmetisch definierte Gruppen mit Galoisoperation, Invent. Math. 48 (1978), no. 2, 185–205 (German). MR 507801, 10.1007/BF01390250
  • [27] J. Rohlfs, The Lefschetz number of an involution on the space of classes of positive definite quadratic forms, Comment. Math. Helv. 56 (1981), no. 2, 272–296. MR 630954, 10.1007/BF02566213
  • [28] -, Lefschetz numbers for automorphisms of finite order on arithmetic groups, in preparation.
  • [29] Jürgen Rohlfs and Birgit Speh, Automorphic representations and Lefschetz numbers, Ann. Sci. École Norm. Sup. (4) 22 (1989), no. 3, 473–499. MR 1011990
  • [30] J. Rohlfs and B. Speh, Lefschetz numbers and twisted stabilized orbital integrals, Math. Ann. 296 (1993), no. 2, 191–214. MR 1219899, 10.1007/BF01445102
  • [31] Jean-Pierre Serre, Cohomologie galoisienne, With a contribution by Jean-Louis Verdier. Lecture Notes in Mathematics, No. 5. Troisième édition, vol. 1965, Springer-Verlag, Berlin-New York, 1965 (French). MR 0201444
  • [32] Robert Steinberg, Endomorphisms of linear algebraic groups, Memoirs of the American Mathematical Society, No. 80, American Mathematical Society, Providence, R.I., 1968. MR 0230728
  • [33] Jacques Tits, Tabellen zu den einfachen Lie Gruppen und ihren Darstellungen, Springer-Verlag, Berlin-New York, 1967 (German). MR 0218489

Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC: 11F75, 55N45

Retrieve articles in all journals with MSC: 11F75, 55N45


Additional Information

DOI: https://doi.org/10.1090/S0894-0347-1993-1186963-2
Article copyright: © Copyright 1993 American Mathematical Society