NON-ISOGENOUS ABELIAN VARIETIES SHARING THE SAME DIVISION FIELDS

摘要

Two abelian varieties A1, A2 over a number field K are strongly iso-Kummerian if the torsion fields K(A1[d]) and K(A2[d]) coincide for all d >= 1. For all g >= 4 we construct geometrically simple, strongly iso-Kummerian g-dimensional abelian varieties over number fields that are not geometrically isogenous. We also discuss related examples and put significant constraints on any further iso-Kummerian pair.