Finiteness of Mordell-Weil Groups of Kuga Fiber Spaces of Abelian Varieties

Abstract

In this paper, we will study Mordell-Weil groups of Kuga fiber spaces of abelian varieties associated to the standard symplectic representation classified by Satake. We will show the finiteness theorem for them with a few exceptions by using the Hodge theory and Borel-Wallach's vanishing theorem.