Normed Fiber Functors

2022/03/31 by Paul Ziegler, Ziegler, Paul
Mathematics · #14L15 #20E42 #20G05 #51E24 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2203.17073

openalex publication_date 2022/03/31 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

By Goldman-Iwahori, the Bruhat-Tits building of the general linear group GL_n over a local field ℓ can be described as the set of non-archimedean norms on ℓⁿ. Via a Tannakian formalism, we generalize this picture to a description of the Bruhat-Tits building of an unramified reductive group G over ℓ 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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