Abstract

In this paper, we investigate the existence of an elementary abelian closure in characteristic not 2 for biquadratic extensions. We discover that it exists for any non-cyclic extension. We make use of it to obtain a classification for this class of extensions up to isomorphism via descent. This permits us to describe the geometry of this moduli space in group theoretic terms. We also provide two families of polynomials with two parameters that can describe any quartic extensions.

中文翻译：

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非循环双二次域扩展的模空间几何

摘要

在本文中，我们研究了双二次扩张的特征非 2 ​​的初等交换闭包的存在性。我们发现对于任何非循环扩展它都存在。我们利用它来获得此类扩展到通过下降同构的分类。这使我们能够用群论术语来描述这个模空间的几何形状。我们还提供了两个具有两个参数的多项式族，可以描述任何四次扩展。