局部體和總體體上的布勞爾群之算術
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Date
2012
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Abstract
我們研究布勞爾群的算術性質，交積代數，循環代數以及它們之間的連結。
在第一節中，我們將知道一個體的布勞爾群中的每一個類都可以用一個在此
體上的中央簡易代數表現。
在第二節中，我們對交積代數有澈底地討論。
在第三節中，我們討論循環代數。
在第四節中，我們探索在局部體上的循環代數與以此體為中心並有有限指數
的偏體之間的關係。
在最後一節中，我們考慮在總體體上的中央簡易代數。
We study some arithmetical properties of Brauer groups, crossed-product algebras, cyclic algebras, and the connection between them. In §1, we will show that each class in the Brauer group of a field K is represented by a central simple K-algebra. In §2, we begin with a thorough discussion of crossed- product algebras. In §3, we discuss the cyclic algebras. In §4, we explore the relations between cyclic algebras over a local field K and skewfields with center K and finite index. In §5, we consider central simple algebras over global fields.
We study some arithmetical properties of Brauer groups, crossed-product algebras, cyclic algebras, and the connection between them. In §1, we will show that each class in the Brauer group of a field K is represented by a central simple K-algebra. In §2, we begin with a thorough discussion of crossed- product algebras. In §3, we discuss the cyclic algebras. In §4, we explore the relations between cyclic algebras over a local field K and skewfields with center K and finite index. In §5, we consider central simple algebras over global fields.
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布勞爾群, 哈斯範數定理, 格朗沃-王定理, 哈斯不變量, Brauer group, Hasse norm theorem, Grunwald-Wang theorem, Hasse invariant