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Integral points for groups of multiplicative type. (English) Zbl 1282.11022
Summary: We construct a finite subgroup of Brauer–Manin obstruction for detecting the existence of integral points on integral models of homogeneous spaces of linear algebraic groups of multiplicative type. As an application, the strong approximation theorem for linear algebraic groups of multiplicative type is established. Moreover, the sum of two integral squares over some quadratic fields is discussed.

11E72 Galois cohomology of linear algebraic groups
11G35 Varieties over global fields
14F22 Brauer groups of schemes
14G25 Global ground fields in algebraic geometry
20G30 Linear algebraic groups over global fields and their integers
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