 About 30,000 results  books.google.com This milestone work on the arithmetic theory of linear algebraic groups is now available in English for the first time. 

 books.google.com If G is defined over an algebraic number field or over a field of algebraic functions
in one variable, then there arise problems about the arithmetic properties of G,
the study of which is the subject of the arithmetic theory of linear algebraic groups
... 

 books.google.com Therefore T(a, b) is not stably rational over Q. This is the simplest example of a
linear algebraic group which is not rational over Q. Consider two cases. ... any
valuation v of Q. 2) There is a decomposition group of order 4, for example, L I Q(
§), is I 1, L = Q(\/:I, Class field theory tells ... Another arithmetic characteristic of G
arises when studying the set H l (k, G) of principal homogeneous spaces (PHS) of
G. 

 books.google.com Introduction The arithmetic theory of linear algebraic groups was established as
an independent field of mathematics within the last decade. One of its
characteristic features is a deep connection with many areas of mathematics, in
particular ... 

 books.google.com Proceedings of the International Conference on the Algebraic and Arithmetic
Theory of Quadratic Forms, December ... research network “Algebraic KTheory,
Linear Algebraic Groups and Related Structures” HPRNCT200200287, and by
the ... 

 books.google.com For studying arithmetic groups, theory of linear algebraic groups is essential.
Linear algebraic groups also provide a natural class of Lie groups and put real
Lie groups and padic Lie groups on the same footing. The reduction theory of ... 

 books.google.com C. Moore, [1] Group extensions of padic and adelic linear groups. Inst. Hautes ...
[2] Theory of algebraic linear groups and periodic groups. ... V. P. Platonov, M. V.
Milovanov, [l] Determination of algebraic groups by arithmetic subgroups. Dokl ... 

 books.google.com ... Algebraic group, Algebraic torus, Anisotropic group; Arithmetic group; Borel
subgroup; Bruhat decomposition; Congruence problem; Diagonal group, Lie
group; Linear algebraic groups, arithmetic theory of; Linear group, Mumford
hypothesis ... 

 books.google.com The arithmetic subgroups defined in this more general case are also
commensurable with “integral” elements. ... Alternatively, suppose that G is a Q
simple linear algebraic group such that its real locus G can be written as a
product G = G1 X ... 

 books.google.com On Conformal Field Theories, Discrete Groups and Renormalization Pierre E.
Cartier, Bernard Julia, Pierre Moussa, ... general theory of algebraic groups, one
could speak of the arithmetic subgroups of any linear algebraic group over Q.
Borel ... 

 