Geodesic
Some applications of Hasse principle for pseudoglobal fields
Algebra and discrete mathematics, no. 2 (2004), pp. 1-8.

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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.
Keywords: algebraic function field, Hasse principle, quadratic form. 
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     title = {Some applications of {Hasse} principle for pseudoglobal fields},
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V. Andriychuk. Some applications of Hasse principle for pseudoglobal fields. Algebra and discrete mathematics, no. 2 (2004), pp. 1-8. http://geodesic.mathdoc.fr/item/ADM_2004_2_a1/