算术方案的Hilbert性质

IF 0.5 3区数学 Q3 MATHEMATICS

Acta Arithmetica Pub Date : 2022-12-02 DOI:10.4064/aa211214-16-11

Cedric Luger

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引用次数: 1

摘要

通过要求近整点的集合(由Vojta定义)是非薄的，我们将域上变化的通常希尔伯特性质推广到积分域上的算术格式。然后，通过证明具有Hilbert性质的算术格式的积和有限覆盖的几个结构结果，推广了barry - soroker - fehm - petersen和Corvaja-Zannier的结果。

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The Hilbert property for arithmetic schemes

We extend the usual Hilbert property for varieties over fields to arithmetic schemes over integral domains by demanding the set of near-integral points (as defined by Vojta) to be non-thin. We then generalize results of Bary-Soroker-Fehm-Petersen and Corvaja-Zannier by proving several structure results related to products and finite \'{e}tale covers of arithmetic schemes with the Hilbert property.

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