An explicit Abelian surface with maximal Galois action

Quinn Greicius; Aaron Landesman

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arXiv · 1804.00032

An explicit Abelian surface with maximal Galois action

Quinn Greicius·Aaron Landesman

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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 $\operatorname{Gal}(\overline{K}/K)$ on the Jacobian of $C$ has image $\operatorname{GSp}_4(\widehat{\mathbb Z})$.

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Quinn Greicius, Aaron Landesman. 2018-03-30. An explicit Abelian surface with maximal Galois action. https://arxiv.org/abs/1804.00032

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