About the obstacle to proving the Baum–Connes conjecture without coefficient for a non-cocompact lattice in 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](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jncg-volume-10-issue-4.png&w=3840&q=90)
Abstract
We introduce property and prove it for some non-cocompact lattice in in a local field of finite characteristic. We show that property for a non-cocompact lattice in a higher rank almost simple algebraic group in a local field is an obstacle to proving the Baum Connes conjecture without coefficient for with known methods, and this is stronger than the well-known fact that 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 in a local field. J. Noncommut. Geom. 10 (2016), no. 4, pp. 1243–1268
DOI 10.4171/JNCG/259