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

Rony A. Bitan; Ralf Köhl

doi:10.7169/facm/2015.53.2.4

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

Rony A. Bitan, Ralf Köhl

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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_∞(G) of types in one orbit of a special vertex in the Bruhat-Tits building of G_∞( ^K_∞) for some place 1 and the class number h_∞(G) of G at ∞.

Original language	English
Pages (from-to)	215-247
Number of pages	33
Journal	Functiones et Approximatio, Commentarii Mathematici
Volume	53
Issue number	2
DOIs	https://doi.org/10.7169/facm/2015.53.2.4
State	Published - 1 Dec 2015
Externally published	Yes

Bibliographical note

Publisher Copyright:
© Uniwersytet im. Adama Mickiewicza w Poznaniu Wydawnictwo Naukowe UAM, Poznan 2015.

Keywords

Bruhat-Tits building
Class number
Relative Tamagawa number
Special vertex

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10.7169/facm/2015.53.2.4

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AB - Let G be a semisimple almost simple group defined over a global function field K, not anisotropic of type An. We express the (relative) Tamagawa number of G in terms of local data, including the number t∞(G) of types in one orbit of a special vertex in the Bruhat-Tits building of G∞( ^K∞) for some place 1 and the class number h∞(G) of G at ∞.

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KW - Special vertex

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

Abstract

Bibliographical note

Keywords

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