Recipes to compute the algebraic K-theory of Hecke algebras of reductive p-adic groups

Bartels, Arthur¹ ; Lück, Wolfgang²

¹Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Münster, Germany
²Mathematisches Institut, Universität Bonn, Bonn, Germany

Algebraic and Geometric Topology, Tome 25 (2025) no. 2, pp. 1133-1154

Résumé

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 tools 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.

Détail

DOI : 10.2140/agt.2025.25.1133

Keywords: algebraic $K$-theory of Hecke algebras, reductive $p$-adic groups, Farrell–Jones conjecture

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