Some applications of Hasse principle for pseudoglobal fields

V. Andriychuk


Some corollaries of the Hasse principle for Brauer group of a pseudoglobal field are obtained. In particular we prove Hasse-Minkowski theorem on quadratic forms over pseudoglobal field and the Hasse principle for quadratic forms of rank 2 or 3 over the field of fractions of an excellent two-dimensional henselian local domain with pseudofinite residue field. It is considered also the Galois group of maximal \(p\)-extensions of a pseudoglobal field.


algebraic function field, Hasse principle, quadratic form

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