Recipes to compute the algebraic K-theory of Hecke algebras of reductive p-adic groups
arXiv:2306.01510 · doi:10.2140/agt.2025.25.1133
Abstract
We compute the algebraic K-theory of the Hecke algebra of a reductive p-adic group G using the fact that the Farrell-Jones Conjecture is known in this context. The main tool will be the properties of the associated Bruhat-Tits building and an equivariant Atiyah-Hirzebruch spectral sequence. In particular the projective class group can be written as the colimit of the projective class groups of the compact open subgroups of G.
20 pages, final version, to appear in Algebraic and Geometric Topology