caa a22 4500 47573825X CHVBK 20180406123452.0 cr unu---uuuuu 170329e20000401xx s 000 0 eng 10.1007/s002220050360 doi (NATIONALLICENCE)springer-10.1007/s002220050360 Dat J.-F Université Paris VII, Département de Mathématiques, Case 7012, 2, place Jussieu, 74251 Paris, France, France aut On the K0 of a p-adic group [Elektronische Daten] [J.-F. Dat] Abstract. : This article deals with various topics related with Grothendieck groups, invariant distributions, parabolic and compact inductions... for a p-adic group G. The main result is a description of the K 0 of the Hecke algebra ℋ of G in terms of discrete series of Levi subgroups, which has an interesting behavior with regard to parabolic restriction and induction. A similar description - but no more compatible with these parabolic functors - is obtained for $\overline{\mathcal{H}}$ =ℋ/[ℋ,ℋ] and the Hattori rank map gets an easy description in this dictionary.¶We follow a beautiful idea of J. Bernstein consisting in comparing two natural filtrations on these objects, one of combinatorial nature and one of topological nature. The combinatorial filtrations are related to the structure of Levi subgroupsin G and have counterparts concerning many classical objects of interest as the Grothendieck group of finite length G-modules R(G), the set Ω sr of regular semi-simple conjugacy classes, and the variety Θ(G) of infinitesimal characters. These filtrations will turn out to be "compatible”, in a sense to be specified, with regard to all the classical operations or morphisms between these objects. Springer-Verlag Berlin Heidelberg, 2000 Inventiones mathematicae Springer Berlin Heidelberg 140/1(2000-04-01), 171-226 0020-9910 140:1<171 2000 140 222 https://doi.org/10.1007/s002220050360 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s002220050360 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Dat J.-F Université Paris VII, Département de Mathématiques, Case 7012, 2, place Jussieu, 74251 Paris, France, France aut NATIONALLICENCE 773 0- Inventiones mathematicae Springer Berlin Heidelberg 140/1(2000-04-01), 171-226 0020-9910 140:1<171 2000 140 222 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer