Prehomogeneous vector spaces and field extensions
Prehomogeneous vector spaces and field extensions
复制标题
预齐次向量空间和域扩展
DOI：
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发表时间：
1992
期刊：
影响因子：
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通讯作者：
Akihiko Yukie
中科院分区：
文献类型：
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作者：
David J. Wright;Akihiko Yukie
设k是特征不等于2，3，5的无限域。本文构造了从某些非齐次向量空间的轨道集到K的Galois扩张的同构类集的自然映射，并证明了该映射的逆象与Galois同态的共轭类是双射对应的。
SummaryLetk be an infinite field of characteristic not equal to 2, 3, 5. In this paper, we construct a natural map from the set of orbits of certain prehomogeneous vector spaces to the set of isomorphism classes of Galois extensions ofk which are splitting fields of equations of certain degrees, and prove that the inverse image of this map corresponds bijectively with conjugacy classes of Galois homomorphisms.