Iwasawa theory for the symmetric square of an elliptic curve

In my talk, I will explain how one can use the Euler system associated to the Asai representation of a quadratic Hilbert modular form to study the arithmetic of the symmetric square of an elliptic curve over Q. In particular, we prove one inclusion of the cyclotomic Iwasawa Main Conjecture, and we give a new proof of the finiteness of the Bloch—Kato Selmer group over Q. This is work in progress with David Loeffler.