Cocenters of $p$-adic groups, III: Elliptic and rigid cocenters

Abstract

In this paper, we show that the elliptic cocenter of the Hecke algebra of a connected reductive group over a nonarchimedean local field is contained in the rigid cocenter. As applications, we prove the trace Paley-Wiener theorem and the abstract Selberg principle for mod-$l$ representations.

23 pages. Proof of Proposition 2.9 is corrected

References in corpus (2)

• Cocenters of $p$-adic groups, I: Newton decomposition
• Cocenter of $p$-adic groups, II: induction map

Cited by in corpus (2)

• Cocenters of $p$-adic groups, I: Newton decomposition
• Jordan Decompositions of cocenters of reductive $p$-adic groups