Functiones et Approximatio Commentarii Mathematici

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

Rony A. Bitan and Ralf Köhl (né Gramlich)

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Abstract

Let $G$ be a semisimple almost simple group defined over a global function field $K$, not anisotropic of type $A_n$. We express the (relative) Tamagawa number of $G$ in terms of local data, including the number $t_\infty(G)$ of types in one orbit of a special vertex in the Bruhat--Tits building of $G_\infty(\hat{K}_\infty)$ for some place $\infty$ and the class number $h_\infty(G)$ of $G$ at $\infty$.

Article information

Source
Funct. Approx. Comment. Math., Volume 53, Number 2 (2015), 215-247.

Dates
First available in Project Euclid: 17 December 2015

Permanent link to this document
https://projecteuclid.org/euclid.facm/1450389053

Digital Object Identifier
doi:10.7169/facm/2015.53.2.4

Mathematical Reviews number (MathSciNet)
MR3435798

Zentralblatt MATH identifier
06862326

Subjects
Primary: 20G25: Linear algebraic groups over local fields and their integers
Secondary: 20G10: Cohomology theory 20E42: Groups with a $BN$-pair; buildings [See also 51E24] 51E24: Buildings and the geometry of diagrams

Keywords
relative Tamagawa number Bruhat-Tits building class number special vertex

Citation

Bitan, Rony A.; Köhl (né Gramlich), Ralf. A building-theoretic approach to relative Tamagawa numbers of semisimple groups over global function fields. Funct. Approx. Comment. Math. 53 (2015), no. 2, 215--247. doi:10.7169/facm/2015.53.2.4. https://projecteuclid.org/euclid.facm/1450389053


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