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- W2307639361 abstract "Let $k$ be a number field and let $mathcal{G}$ be a commutative algebraic group defined over $k$. Let $p$ be a prime number and let ${mathcal{G}}[p]$ denote the $p$-torsion subgroup of $mathcal{G}$. It is well-known that ${mathcal{G}}[p]cong ({mathbb{Z}}/p{mathbb{Z}})^n$, for some positive integer $n$ depending only on $mathcal{G}$. We prove that for every $n$, there exists a prime $p_n$ depending only on $n$, such that if $mathcal{G}$ does not admit a $k$-rational isogeny of degree $p^h$, for all $1leq hleq n-1$, then the local-global divisibility by $p$ holds in ${mathcal{G}}(k)$, for all primes $p>p_n$. In particular this is true for all abelian varieties and generalizes some previous result showed for elliptic curves." @default.
- W2307639361 created "2016-06-24" @default.
- W2307639361 creator A5004296698 @default.
- W2307639361 date "2016-03-18" @default.
- W2307639361 modified "2023-09-27" @default.
- W2307639361 title "Divisibility of points in commutative algebraic groups" @default.
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