Duke Mathematical Journal

Symplectic modular symbols

Paul E. Gunnells

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Article information

Duke Math. J. Volume 102, Number 2 (2000), 329-350.

First available in Project Euclid: 17 August 2004

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F75: Cohomology of arithmetic groups
Secondary: 11F80: Galois representations


Gunnells, Paul E. Symplectic modular symbols. Duke Math. J. 102 (2000), no. 2, 329--350. doi:10.1215/S0012-7094-00-10226-8. http://projecteuclid.org/euclid.dmj/1092749298.

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  • G. Allison, A. Ash, and E. Conrad, Galois representations, Hecke operators and the mod-$p$ cohomology of ${\GL}(3,{\Z})$ with twisted coefficients, Experiment. Math. 7 (1998), 361--390.
  • A. Ash, A note on minimal modular symbols, Proc. Amer. Math. Soc. 96 (1986), 394--396.
  • --. --. --. --., Galois representations attached to mod $p$ cohomology of ${\GL}(n,{{\Z}})$, Duke Math. J. 65 (1992), 235--255.
  • A. Ash and M. McConnell, Experimental indications of three-dimensional Galois representations from the cohomology of ${{\SL}}(3,{\Z})$, Experiment. Math. 1 (1992), 209--223.
  • A. Ash, R. Pinch, and R. Taylor, An $\widehat{A_4}$ extension of ${\Q}$ attached to a non-selfdual automorphic form on ${\GL}(3)$, Math. Ann. 291 (1991), 753--766.
  • A. Ash and L. Rudolph, The modular symbol and continued fractions in higher dimensions, Invent. Math. 55 (1979), 241--250.
  • A. Ash and W. Sinnott, An analogue of Serre's conjecture for Galois representations and Hecke eigenclasses in the mod-$p$ cohomology of ${\GL}(n,{\Z})$, preprint, available at http://can.dpmms.cam.ac.uk/Algebraic-Number-Theory/0185/index.html.
  • A. Borel and J.-P. Serre, Corners and arithmetic groups, Comm. Math. Helv. 48 (1973), 436--491.
  • I. M. Gelfand and V. V. Serganova, On the general definition of a matroid and a greedoid, Dokl. Akad. Nauk SSSR 292 (1987), 15--20.
  • P. Gunnells, Computing Hecke eigenvalues below the cohomological dimension, to appear in Experiment. Math.
  • R. MacPherson and M. McConnell, ``Classical projective geometry and modular varieties'' in Proceedings of the JAMI Inaugural Conference, Johns Hopkins University Press, Baltimore, 1989, 237--290.
  • --. --. --. --., Explicit reduction theory for Siegel modular threefolds, Invent. Math. 111 (1993), 575--625.
  • J. Schwermer, On arithmetic quotients of the Siegel upper half space of degree two, Compositio Math. 58 (1986), 233--258.
  • --. --. --. --., Eisenstein series and cohomology of arithmetic groups: the generic case, Invent. Math. 116 (1994), 481--511.
  • --. --. --. --., On Euler products and residual Eisenstein cohomology classes for Siegel modular varieties, Forum Math. 7 (1995), 1--28.
  • J. Tits, Sur la trialité et certains groupes qui s'en déduisent, Inst. Hautes Études Sci. Publ. Math. (1959), 13--60.
  • --------, Buildings of Spherical Type and Finite BN-Pairs, Lecture Notes in Math. 386, Springer-Verlag, Berlin, 1974.
  • B. van Geemen and J. Top, A non-selfdual automorphic representation of ${\GL} \sb 3$ and a Galois representation, Invent. Math. 117 (1994), 391--401.