On the algebraic K-theory of Hecke algebras

Arthur Bartels; Wolfgang Lueck

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arXiv · 2204.07982

On the algebraic K-theory of Hecke algebras

Arthur Bartels·Wolfgang Lueck

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Abstract

Consider a totally disconnected group G, which is covirtually cyclic, i.e., contains a normal compact open subgroup L such that G/L is infinite cyclic. We establish a Wang sequence, which computes the algebraic K-groups of the Hecke algebra of G in terms of the one of L, and show that all negative K-groups vanish. This confirms the K-theoretic Farrell-Jones Conjecture for the Hecke algebra of G in this special case. Our ultimate long term goal is to prove it for any closed subgroup of any reductive p-adic group. The results of this paper will play a role in the final proof.

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BibTeX RIS

Arthur Bartels, Wolfgang Lueck. 2022-04-17. On the algebraic K-theory of Hecke algebras. https://arxiv.org/abs/2204.07982

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