Finite galois modules
Copyright policy )Finite galois modules
A single general formula is given for the weak approximation in algebraic tori over global fields. We calculate the first cohomology group for the torus of an embedding problem of fields with Abelian kernel, the coefficients being the Picard group of a nonsingular projective model of the torus. The Tamagawa numbers of a certain class of reductive groups are calculated.
algebraic torus over global field, group of weak approximation, Galois theory, Local deformation theory, Artin approximation, etc., embedding problem of number fields, Galois module, Picard group, Special surfaces, weak approximation in algebraic tori, Tamagawa numbers, Global ground fields in algebraic geometry, torus over global fields
algebraic torus over global field, group of weak approximation, Galois theory, Local deformation theory, Artin approximation, etc., embedding problem of number fields, Galois module, Picard group, Special surfaces, weak approximation in algebraic tori, Tamagawa numbers, Global ground fields in algebraic geometry, torus over global fields
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