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Optimal quotients and surjections of Mordell-Weil groups. (English) Zbl 1417.11113
Summary: Answering a question of Ed Schaefer, we show that if $$J$$ is the Jacobian of a curve $$C$$ over a number field, if $$s$$ is an automorphism of $$J$$ coming from an automorphism of $$C$$, and if $$u$$ lies in $$\mathbb{Z} [s] \subseteq \operatorname{End} J$$ and has connected kernel, then it is not necessarily the case that $$u$$ gives a surjective map from the Mordell-Weil group of $$J$$ to the Mordell-Weil group of its image.
##### MSC:
 11G10 Abelian varieties of dimension $$> 1$$ 11G05 Elliptic curves over global fields 11G30 Curves of arbitrary genus or genus $$\ne 1$$ over global fields 11G35 Varieties over global fields
##### Keywords:
Jacobian; Mordell-Weil group; automorphism
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##### References:
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