Ashay Burungale (U. of Arizona)
Horizontal variation of Mordell-Weil groups

Abstract: Let F be a totally real field. For a CM quadratic extension K/F, let H_K be the corresponding Hilbert class field. Let \Theta be an infinite collection of CM quadratic extensions of F. For a \GL_2-type abelian variety A/F, we discuss results on the variation of Mordell-Weil groups A(H_K) as K \in \Theta varies (joint with Ye Tian). Time permitting, we discuss p-indivisibility of relevant Heegner points under mild hypotheses (joint with Haruzo Hida and Ye Tian).