Torsion of abelian varieties, Weil classes and cyclotomic extensions

Original · EN

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.