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arXiv · 2306.01510

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

Arthur Bartels·Wolfgang Lueck
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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.

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Arthur Bartels, Wolfgang Lueck. 2023-06-02. Recipes to compute the algebraic K-theory of Hecke algebras of reductive p-adic groups. https://doi.org/10.2140/agt.2025.25.1133

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