Technique de descente et théorèmes d'existence en géométrie algébriques. II. Le théorème d'existence en théorie formelle des modules
We define the algebraic fundamental group π 1(G) of a reductive group scheme G over an arbitrary non-empty base scheme and show that the resulting functor G↦ π1(G) is exact.
Let and be smooth and projective varieties over a field finitely generated over , and let and be the varieties over an algebraic closure of obtained from and , respectively, by extension of the ground field. We show that the Galois invariant subgroup of Br Br( has finite index in the Galois invariant subgroup of Br. This implies that the cokernel of the natural map Br Br Br is finite when is a number field. In this case we prove that the Brauer–Manin set of the product of...