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 ) 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. 1243–1268DOI 10.4171/JNCG/259