Iwasawa Theory for Elliptic Curves along the Anticyclotomic Zp-Extension

Mazur proved in 1972 an asymptotic formula for the p-primary part of the Tate-Shafarevich group of p-ordinary abelian varieties along the cyclotomic Zp-extension of Q. In this talk we will discuss analogous results for supersingular elliptic curves along the anticylotmic Zp-extension of an imaginary quadratic field satisfying the (generalized) Heegner hypothesis.  The proof of this result relies on the analysis of Heegner points and BDP-Selmer groups. We will discuss both objects and their properties briefly.