Эта публикация цитируется в 3 статьях

RESEARCH ARTICLE

Some applications of Hasse principle for pseudoglobal fields

V. Andriychuk

Department of Mathematics and Mechanic, Lviv Ivan Franko University, Lviv, Ukraine

Аннотация: 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.

Ключевые слова: algebraic function field, Hasse principle, quadratic form.

MSC: 11R58, 11EA12, 11R37

Поступила в редакцию: 24.02.2004
Исправленный вариант: 01.06.2004

Язык публикации: английский

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