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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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

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

First available in Project Euclid: 17 December 2015

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Zentralblatt MATH identifier

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

relative Tamagawa number Bruhat-Tits building class number special vertex


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.

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