一级还原 p-adic 群的 K 理论与伯恩斯坦区块

arXiv - MATH - K-Theory and Homology Pub Date : 2024-07-20 DOI:arxiv-2407.14929

Maximilian Tönies

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摘要

我们根据某些紧凑开子群的 K 理论，证明了具有正则系数的一阶还原 p-adic 群的 K 理论谱的临界公式。此外，在复数情况下，我们利用罗氏提供的类型构造证明，如果群是分裂的，这个结果可以改进为得到每个主系伯恩斯坦块的 K 理论谱公式。

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

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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arXiv - MATH - K-Theory and Homology

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