大多数完全真实的领域没有通用形式或诺斯考特属性

arXiv - MATH - Number Theory Pub Date : 2024-09-17 DOI:arxiv-2409.11082

Nicolas Daans, Vitezslav Kala, Siu Hang Man, Martin Widmer, Pavlo Yatsyna

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引用次数: 0

摘要

我们证明，在所有具有可构造拓扑的全实数域空间中，容许普遍二次型或具有诺斯科特性质的域集合是微不足道的。我们的主要工具是一个新定理，即由给定秩的二次网格代表的完全正单元的平方类的数目。

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Most totally real fields do not have universal forms or Northcott property

We show that, in the space of all totally real fields equipped with the constructible topology, the set of fields that admit a universal quadratic form, or have the Northcott property, is meager. The main tool is a new theorem on the number of square classes of totally positive units represented by a quadratic lattice of a given rank.

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arXiv - MATH - Number Theory

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