Skip to main content
SpringerLink
Log in

Cohomology of discrete groups in harmonic cochains on buildings

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. Alon and E. de Shalit,On the cohomology of Drinfel’d’s p-adic symmetric domain, Israel Journal of Mathematics129 (2002), 1–20.

    Article  MATH  MathSciNet  Google Scholar 

  2. R. Coleman and A. Iovita,The Frobenius and the monodromy operators for curves and abelian varieties, Duke Mathematical Journal97 (1999), 171–215.

    Article  MATH  MathSciNet  Google Scholar 

  3. E. de Shalit,Residues on buildings and de Rham cohomology of p-adic symmetric domains, Duke Mathematical Journal106 (2000), 123–191.

    Article  Google Scholar 

  4. E. de Shalit,Eichler cohomology and periods of modular forms on p-adic Schottky groups, Journal für die reine und angewandte Mathematik400 (1989), 3–31.

    Article  MATH  Google Scholar 

  5. H. Garland,p-adic curvature and the cohomlogy of discrete subgroups of p-adic groups, Annals of Mathematics (2)97 (1973), 375–423.

    Article  MathSciNet  Google Scholar 

  6. O. Hyodo,On the de Rham-Witt complex attached to a semi-stable family, Compositio Mathematica78 (1991), 241–260.

    MATH  MathSciNet  Google Scholar 

  7. A. Iovita and M. Spiess,Logarithmic differential forms on p-adic symmetric spaces, Duke Mathematical Journal110 (2000), 253–278.

    Article  MathSciNet  Google Scholar 

  8. A. Mokrane,La suite spectrale des poids en cohomologie de Hyodo-Kato, Duke Mathematical Journal72 (1993), 301–337.

    Article  MATH  MathSciNet  Google Scholar 

  9. P. Schneider,The cohomology of local systems on p-adically uniformized varieties, Mathematische Annalen293 (1992), 623–650.

    Article  MATH  MathSciNet  Google Scholar 

  10. P. Schneider and U. Stuhler,The cohomology of p-adic symmetric spaces, Inventiones Mathematicae105 (1991), 47–122.

    Article  MATH  MathSciNet  Google Scholar 

  11. P. Schneider and U. Stuhler,Resolutions for smooth representations of the general linear group over a local field, Journal für die reine und angewandte Mathematik436 (1993), 19–32.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, The Hebrew University of Jerusalem, 91904, Givat Ram, Jerusalem, Israel

    Gil Alon & Ehud de Shalit

Authors
  1. Gil Alon
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ehud de Shalit
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gil Alon.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alon, G., de Shalit, E. Cohomology of discrete groups in harmonic cochains on buildings. Isr. J. Math. 135, 355–380 (2003). https://doi.org/10.1007/BF02776064

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02776064

Keywords

Search

Navigation