A building-theoretic approach to relative Tamagawa numbers of quasi-split semisimple groups over global function fields

2013/09/29 by Rony A. Bitan, Rony Bitan, Bitan, Rony +2
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.1309.7641

openalex publication_date 2013/09/29 · arxiv created 2014/09/02 · arxiv updated 2014/09/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let G be a semisimple quasi-split group defined over a global function field. We express the relative Tamagawa number of G in terms of local data including the number of types of special vertices in one orbit of the Bruhat-Tits building over some completion with respect to a place and the class number of G at that place.

Citations

• Abelian class groups of reductive group schemes

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