$2$-adic Representations of Elliptic Curves over $\mathbb{Q}_2$

Jose Castro-Moreno; Nuno Freitas

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arXiv · 2610.25332

$2$-adic Representations of Elliptic Curves over $\mathbb{Q}_2$

Jose Castro-Moreno·Nuno Freitas

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Abstract

We provide a complete classification of the rational $2$-adic Tate modules $V_2(E)$ of elliptic curves $E/\mathbb{Q}_2$ with potentially good reduction. The classification is given in terms of the filtered $(φ,\mathrm{Gal})$-modules associated to $V_2(E)$ via Fontaine's functor $D_{pcris}^{*}$.

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BibTeX RIS

Jose Castro-Moreno, Nuno Freitas. 2026-10-18. $2$-adic Representations of Elliptic Curves over $\mathbb{Q}_2$. https://arxiv.org/abs/2610.25332

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