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arXiv · 2407.14929

K-theory of rank one reductive p-adic groups and Bernstein blocks

Maximilian Tönies
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Abstract

We prove a colimit formula for the K-theory spectra of reductive p-adic groups of rank one with regular coefficients in terms of the K-theory of certain compact open subgroups. Furthermore, in the complex case, we show, using the construction of types provided by Roche, that this result can be improved to obtain a formula for the K-theory spectrum of every principal series Bernstein block if the group is split.

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Maximilian Tönies. 2024-07-20. K-theory of rank one reductive p-adic groups and Bernstein blocks. https://arxiv.org/abs/2407.14929

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