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- W3086811699 abstract "Let $G$ be a commutative connected algebraic group over a number field $K$, let $A$ be a finitely generated and torsion-free subgroup of $G(K)$ of rank $r>0$ and, for $n>1$, let $K(n^{-1}A)$ be the smallest extension of $K$ inside an algebraic closure $overline K$ over which all the points $Pin G(overline K)$ such that $nPin A$ are defined. We denote by $s$ the unique non-negative integer such that $G(overline K)[n]cong (mathbb Z/nmathbb Z)^s$ for all $ngeq 1$. We prove that, under certain conditions, the ratio between $n^{rs}$ and the degree $[K(n^{-1}A):K(G[n])]$ is bounded independently of $n>1$ by a constant that depends only on the $ell$-adic Galois representations associated with $G$ and on some arithmetic properties of $A$ as a subgroup of $G(K)$ modulo torsion. In particular we extend the main theorems of [13] about elliptic curves to the case of arbitrary rank." @default.
- W3086811699 created "2020-09-21" @default.
- W3086811699 creator A5032139656 @default.
- W3086811699 date "2020-09-17" @default.
- W3086811699 modified "2023-09-27" @default.
- W3086811699 title "Radical entanglement for elliptic curves" @default.
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- W3086811699 hasPublicationYear "2020" @default.
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