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Torsion of abelian varieties, Weil classes and cyclotomic extensions

Yuri G. Zarhin
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Abstract

Let $K$ be a field finitely generated over the field of rational numbers, $K(c)$ the extension of $K$ obtained by adjoining all roots of unity, $L$ an infinite Galois extension of $K$, $X$ an abelian variety defined over $K$. We prove that under certain conditions on $X$ and $K$ the existence of infinitely many L-rational points of finite order on $X$ implies that the intersection of $L$ and $K(c)$ has infinite degree over $K$.

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BibTeXRIS

Yuri G. Zarhin. 1997-12-16. Torsion of abelian varieties, Weil classes and cyclotomic extensions. https://arxiv.org/abs/alg-geom/9708007

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