Journal of the Mathematical Society of Japan

Fundamental Hermite constants of linear algebraic groups

Takao WATANABE

Full-text: Open access

Abstract

Let G be a connected reductive algebraic group defined over a global field k and Q a maximal k-parabolic subgroup of G. The constant γ(G,Q,k) attached to (G,Q) is defined as an analogue of Hermite's constant. This constant depends only on G,Q and k in contrast to the previous definition of generalized Hermite constants ([W1]). Some functorial properties of γ(G,Q,k) are proved. In the case that k is a function field of one variable over a finite field, γ(GLn,Q,k) is computed.

Article information

Source
J. Math. Soc. Japan, Volume 55, Number 4 (2003), 1061-1080.

Dates
First available in Project Euclid: 3 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1191418764

Digital Object Identifier
doi:10.2969/jmsj/1191418764

Mathematical Reviews number (MathSciNet)
MR2003760

Zentralblatt MATH identifier
1103.11033

Subjects
Primary: 11R56: Adèle rings and groups
Secondary: 11G35: Varieties over global fields [See also 14G25] 14G25: Global ground fields

Keywords
Hermite constant Tamagawa number linear algebraic group

Citation

WATANABE, Takao. Fundamental Hermite constants of linear algebraic groups. J. Math. Soc. Japan 55 (2003), no. 4, 1061--1080. doi:10.2969/jmsj/1191418764. https://projecteuclid.org/euclid.jmsj/1191418764


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