Torsion of abelian varieties, Weil classes and cyclotomic extensions
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
.