qp -局部系统的退化轨迹:猜想

IF 0.8 4区数学 Q2 MATHEMATICS Expositiones Mathematicae Pub Date : 2023-09-01 DOI:10.1016/j.exmath.2023.05.002

Anna Cadoret

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引用次数: 0

摘要

我们引入了一个关于p进局部系统在数域上光滑变异上退化轨迹的算术稀疏性的猜想，并对Bombieri-Lang猜想进行模化，证明了它是由局部系统所附水平变异几何上的一个猜想推导出来的。我们给出了我们的猜想在算术几何经典问题中的几个应用。最后，我们给出了一些证据，并讨论了一些攻击它的观点，特别是对于由几何产生的p进局部系统。

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Degeneration locus of Qp-local systems: Conjectures

We introduce a conjecture on the arithmetic sparcity of the degeneration locus of a $p$ -adic local system on a smooth variety over a number field and, modulo the Bombieri–Lang conjecture, show that it follows from a conjecture on the geometry of the level varieties attached to the local system. We present a few applications of our conjecture to classical problems in arithmetic geometry. Eventually, we give some evidences and discuss a few perspectives to attack it, in particular for $p$ -adic local systems arising from geometry.

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来源期刊

Expositiones Mathematicae 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

40 days

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