Generating Elements of the Annihilating Ideal for Modular Symbols

Functional Analysis and Its Applications - Tập 37 - Trang 263-272 - 2003
V. A. Bykovskii1
1Khabarovsk Division of the Institute of Applied Mathematics, Far Eastern Division of the Russian Academy of Sciences, Russia

Tóm tắt

In the paper, the concrete generators are found for the annihilating ideal of the modular symbols associated with SL(s;ℤ). Using this result, the (co)homology of subgroups of finite index is evaluated for SL(s;ℤ).

Tài liệu tham khảo

M. Eichler, “Eine Verallgemeinerung der Abelschen Integrale,” Math. Z., 67, 267–298 (1957). G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Princeton Univ. Press, NJ, 1971. Yu. I. Manin, “Parabolic points and zeta functions of modular curves,” Izv. Akad. Nauk SSSR, Ser. Mat., 36, 19–66 (1972). Yu. I. Manin, “Periods of cusp forms and p-adic Hecke series,” Mat. Sb. (N.S.) 92, No. 3, 378–401 (1973). Yu. I. Manin, “Explicit formulas for the eigenvalues of Hecke operators,” Acta Arith., 24, 239–249 (1973). A. Ash and L. Rudolph, “The modular symbol and continued fractions in higher dimensions,” Invent. Math., 55, 241–250 (1979). A. Ash, “Unstable cohomology of SL(n,272–1),” J. Algebra, 167, No. 2, 330–342 (1994). A. Ash and W. Sinnott, “An analogue of Serre's conjecture for Galois representations and Hecke eigenclasses in the mod p cohomology of GL(n, ℤ),” Duke Math. J., 105, No. 2, 1–24 (2000). K. Brown, Cohomology of Groups, Springer-Verlag, New York-Berlin, 1982. A. Borel and J.-P. Serre, “Corners and arithmetic groups,” Comm. Math. Helv., 48, 436–491 (1973). A. Ash, “Cohomology of congruence subgroups of SL(n, ℤ),” Math. Ann., 249, No. 1, 55–73 M. Reeder, “Modular symbols and the Steinberg representation,” In: Cohomology of arithmetic groups and automorphic forms (Luminy-Marseille, 1989), Lect. Notes in Math., Vol. 1447, Springer, Berlin, 1990, pp. 287–302. M. Reeder, “The Steinberg module and the cohomology of arithmetic groups,” J. Algebra, 141, No. 2, 287–315 (1991). C. Soule, “The cohomology of SL 3(ℤ),” Topology, 17, 1–22 (1978).