Number Theory Seminar

Let V be a p-adic Galois representation associated to an elliptic cusp form and let K be an imaginary quadratic field satisfying the classical Heegner hypothesis. It is well-known that by the Euler system of (generalized) Heegner cycles, we can bound the size of the Selmer group associated to V over K. We consider the same problem for V twisted by an anticyclotomic Hecke character psi of K. If p is ordinary for V, a naive twisting argument for the Euler system works to bound the Selmer group for V(psi). However, the situation is different for a non-ordinary prime p. One approach to treat this case is to use the Beilinson-Flach elements. In this talk, I explain another more direct approach by using integral Perrin-Riou twists.