Geometric quadratic Chabauty and p-adic heights

IF 0.8 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae Pub Date : 2023-09-01 DOI:10.1016/j.exmath.2023.05.003

Juanita Duque-Rosero , Sachi Hashimoto , Pim Spelier

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引用次数: 0

Abstract

Let $X$ be a curve of genus $g > 1$ over $Q$ whose Jacobian $J$ has Mordell–Weil rank $r$ and Néron–Severi rank $ρ$ . When $r < g + ρ - 1$ , the geometric quadratic Chabauty method determines a finite set of $p$ -adic points containing the rational points of $X$ . We describe algorithms for geometric quadratic Chabauty that translate the geometric quadratic Chabauty method into the language of $p$ -adic heights and $p$ -adic (Coleman) integrals. This translation also allows us to give a comparison to the (original) cohomological method for quadratic Chabauty. We show that the finite set of $p$ -adic points produced by the geometric method is contained in the finite set produced by the cohomological method, and give a description of their difference.

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几何二次恰布蒂和p进高度

设X是一条g>1 / Q的曲线，它的雅可比矩阵J有Mordell-Weil秩r和n - severi秩ρ。当r<g+ρ−1时，几何二次Chabauty方法确定了包含x的有理点的有限p进点集。我们描述了将几何二次Chabauty方法转换为p进高度和p进(Coleman)积分语言的几何二次Chabauty算法。这种转换也允许我们对二次Chabauty的(原始)上同调方法进行比较。证明了几何方法得到的p进点的有限集合包含在上同调方法得到的有限集合中，并给出了它们之间的差的描述。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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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