Brauer groups of rational function fields
نویسندگان
چکیده
منابع مشابه
On Fields with Finite Brauer Groups
Let K be a field of characteristic 6= 2, let Br(K)2 be the 2primary part of its Brauer group, and let GK(2) = Gal(K(2)/K) be the maximal pro-2 Galois group of K. We show that Br(k)2 is a finite elementary abelian 2-group (Z/2Z), r ∈ N, if and only if GK(2) is a free pro-2 product of a closed subgroup H which is generated by involutions and of a free pro-2 group. Thus, the fixed field of H in K(...
متن کاملBrauer Groups
I define the Brauer group of a field k as similarity classes of central simple algebras over k. Then I introduce non-abelean cohomology and use it to prove that the Brauer group is isomorphic to a certain cohomology group. Brauer groups show up in global class field theory.
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We show that, for all characteristic p global fields k and natural numbers n coprime to the order of the non–p–part of the Picard group Pic0(k) of k, there exists an abelian extension L/k whose local degree at every prime of k is equal to n. This answers in the affirmative in this context a question recently posed by Kisilevsky and Sonn. As a consequence, we show that, for all n and k as above,...
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متن کاملValue Groups, Residue Fields, and Bad Places of Rational Function Fields
We classify all possible extensions of a valuation from a ground field K to a rational function field in one or several variables over K. We determine which value groups and residue fields can appear, and we show how to construct extensions having these value groups and residue fields. In particular, we give several constructions of extensions whose corresponding value group and residue field e...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1979
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1979-14658-5