Israel Journal of Mathematics

, Volume 135, Issue 1, pp 355–380

Cohomology of discrete groups in harmonic cochains on buildings

Authors

    • Institute of MathematicsThe Hebrew University of Jerusalem
  • Ehud de Shalit
    • Institute of MathematicsThe Hebrew University of Jerusalem
Article

DOI: 10.1007/BF02776064

Cite this article as:
Alon, G. & de Shalit, E. Isr. J. Math. (2003) 135: 355. doi:10.1007/BF02776064

Abstract

Modules of harmonic cochains on the Bruhat-Tits building of the projective general linear group over ap-adic field were defined by one of the authors, and were shown to represent the cohomology of Drinfel’d’sp-adic symmetric domain. Here we define certain non-trivial natural extensions of these modules and study their properties. In particular, for a quotient of Drinfel’d’s space by a discrete cocompact group, we are able to define maps between consecutive graded pieces of its de Rham cohomology, which we show to be (essentially) isomorphisms. We believe that these maps are graded versions of the Hyodo-Kato monodromy operatorN.

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Copyright information

© The Hebrew University Magnes Press 2003