ON THE ESSENTIAL TORSION FINITENESS OF ABELIAN VARIETIES OVER TORSION FIELDS
ON THE ESSENTIAL TORSION FINITENESS OF ABELIAN VARIETIES OVER TORSION FIELDS
Abstract The classical Mordell–Weil theorem implies that an abelian variety A over a number field K has only finitely many K -rational torsion points. This finitude of torsion still holds even over the cyclotomic extension $K^{\mathrm {cyc}}=K{\mathbb Q}^{\mathrm {ab}}$ by a result of Ribet. In this article, we consider the …