Normed Fiber Functors

Paul Ziegler

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arXiv · 2203.17073

Normed Fiber Functors

Paul Ziegler

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Abstract

By Goldman-Iwahori, the Bruhat-Tits building of the general linear group $\operatorname{GL}_n$ over a local field $\ell$ can be described as the set of non-archimedean norms on $\ell^n$. Via a Tannakian formalism, we generalize this picture to a description of the Bruhat-Tits building of an unramified reductive group $G$ over $\ell$ as the set of norms on the standard fiber functor of a special parahoric integral model of $G$. We also give a moduli-theoretic description of the parahoric group scheme associated to a point of the building as the group scheme of tensor automorphisms of the lattice chains defined by the corresponding norm.

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BibTeX RIS

Paul Ziegler. 2022-03-31. Normed Fiber Functors. https://arxiv.org/abs/2203.17073

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