Abstract:We introduce a relation between the generator of the Eisenstein ideal in a Hida family and Iwasawa invariants for modular forms and ideal class groups. We introduce our result forcusing on two types of examples
AbstractLet E be a rational elliptic curve and p be an odd prime of good ordinary reduction for E. In 1991 Kolyvagin conjectured that the system of cohomology classes derived from Heegner points on the p-adic Tate module of E over an imaginary quadratic field K is non-trivial. I will talk about joint work with A.Burungale, F.Castella, and C.Skinner, where we prove Kolyvagin's conjecture in the ...