JournalsjncgVol. 10, No. 4pp. 1243–1268

About the obstacle to proving the Baum–Connes conjecture without coefficient for a non-cocompact lattice in Sp4Sp_4 in a local field

  • Benben Liao

    University of Lyon, France
About the obstacle to proving the Baum–Connes conjecture without coefficient for a non-cocompact lattice in $Sp_4$ in a local field cover
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Abstract

We introduce property (TSchur,G,K)(T_\mathrm {Schur},G,K) and prove it for some non-cocompact lattice in Sp4Sp_4 in a local field of finite characteristic. We show that property (TSchur,G,K)(T_\mathrm {Schur},G,K) for a non-cocompact lattice Γ\Gamma in a higher rank almost simple algebraic group in a local field is an obstacle to proving the Baum Connes conjecture without coefficient for Γ\Gamma with known methods, and this is stronger than the well-known fact that Γ\Gamma does not have the property of rapid decay (property (RD)). It is the first example (as announced in [7]) for which all known methods for proving the Baum–Connes conjecture without coefficient fail.

Cite this article

Benben Liao, About the obstacle to proving the Baum–Connes conjecture without coefficient for a non-cocompact lattice in Sp4Sp_4 in a local field. J. Noncommut. Geom. 10 (2016), no. 4, pp. 1243–1268

DOI 10.4171/JNCG/259