Towards a classification of entanglements of Galois representations attached to elliptic curves
نویسندگان
چکیده
Let $E/\mathbb{Q}$ be an elliptic curve, let $\overline{\mathbb{Q}}$ a fixed algebraic closure of $\mathbb{Q}$, and $G\_{\mathbb{Q}}=\text{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$ the absolute Galois group $\mathbb{Q}$. The action $G\_{\mathbb{Q}}$ on adelic Tate module $E$ induces representation $\rho\_E\colon G\_{\mathbb{Q}} \to \text{GL}(2,\widehat{\mathbb{Z}}).$ goal this paper is to explain how image $\rho\_E$ can smaller than expected. To end, we offer theoretic categorization different ways in which entanglement between division fields explained prove several results curves (and more generally, principally polarized abelian varieties) over $\mathbb{Q}$ where occurs extension.
منابع مشابه
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ژورنال
عنوان ژورنال: Revista Matematica Iberoamericana
سال: 2023
ISSN: ['2235-0616', '0213-2230']
DOI: https://doi.org/10.4171/rmi/1424