Finite Group Actions on Siegel Modular Spaces
HTML articles powered by AMS MathViewer
- by K. F. Lai and Ronnie Lee
- Trans. Amer. Math. Soc. 345 (1994), 37-45
- DOI: https://doi.org/10.1090/S0002-9947-94-99998-4
- PDF | Request permission
Abstract:
The theory of nonabelian cohomology is used to show that the set of fixed points of a finite group acting on a Siegel modular space is a union of Shimura varietiesReferences
- Armand Borel and Jacques Tits, Homomorphismes “abstraits” de groupes algébriques simples, Ann. of Math. (2) 97 (1973), 499–571 (French). MR 316587, DOI 10.2307/1970833
- Erhard Gottschling, Über die Fixpunkte der Siegelschen Modulgruppe, Math. Ann. 143 (1961), 111–149 (German). MR 123026, DOI 10.1007/BF01342975
- Erhard Gottschling, Über die Fixpunktuntergruppen der Siegelschen Modulgruppe, Math. Ann. 143 (1961), 399–430 (German). MR 124407, DOI 10.1007/BF01470754
- Sigurđur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962. MR 0145455
- M. Kneser, Lectures on Galois cohomology of classical groups, Tata Institute of Fundamental Research Lectures on Mathematics, No. 47, Tata Institute of Fundamental Research, Bombay, 1969. With an appendix by T. A. Springer; Notes by P. Jothilingam. MR 0340440
- 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, DOI 10.1007/BF02566213
- Ichirô Satake, Algebraic structures of symmetric domains, Kanô Memorial Lectures, vol. 4, Iwanami Shoten, Tokyo; Princeton University Press, Princeton, N.J., 1980. MR 591460
- Jean-Pierre Serre, Cohomologie galoisienne, Lecture Notes in Mathematics, No. 5, Springer-Verlag, Berlin-New York, 1965 (French). With a contribution by Jean-Louis Verdier; Troisième édition, 1965. MR 0201444
- Goro Shimura, Moduli of abelian varieties and number theory, Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965) Amer. Math. Soc., Providence, R.I., 1966, pp. 312–332. MR 0237507
- Goro Shimura, On analytic families of polarized abelian varieties and automorphic functions, Ann. of Math. (2) 78 (1963), 149–192. MR 156001, DOI 10.2307/1970507
- Goro Shimura, Moduli and fibre systems of abelian varieties, Ann. of Math. (2) 83 (1966), 294–338. MR 199190, DOI 10.2307/1970434
- T. A. Springer, Galois cohomology of linear algebraic groups, Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965) Amer. Math. Soc., Providence, R.I., 1966, pp. 149–158. MR 0210714
- André Weil, Algebras with involutions and the classical groups, J. Indian Math. Soc. (N.S.) 24 (1960), 589–623 (1961). MR 136682
Bibliographic Information
- © Copyright 1994 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 345 (1994), 37-45
- MSC: Primary 20G05,, 14K10,, 57S25
- DOI: https://doi.org/10.1090/S0002-9947-94-99998-4