Abstract

We construct an explicit example of a genus 2 curve C over a number field K such that the adelic Galois representation arising from the action of $\mathrm{Gal}(\overline{K}/K)$ on the Jacobian of C has image ${\text{GSp}}_4(\widehat{\mathbb{Z}}).$

中文翻译：

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具有最大伽罗瓦作用的显式阿贝尔曲面

摘要

我们在数域K上构造了一个属 2 曲线C的显式示例，使得由$\mathrm{加尔}(\overline{ķ}/ķ)$在C的雅可比上具有图像${\text{GSP}}_4(\widehat{\mathbb{Z}}).$