Torsion of abelian varieties, Weil classes and cyclotomic extensions

Details Torsion of abelian varieties, Weil classes and cyclotomic extensions Torsion of abelian varieties, Weil classes and cyclotomic extensions

1997-08-04

arxiv.org/abs/alg-geom/9708007v5

Mathematics

Algebraic Geometry

LaTeX 2e 17 pages

Scientific paper

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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