Kolyvagin's method of Euler systems

Kolyvagin uses an Euler system to bound the size of the Selmer group of certain elliptic curves over imaginary quadratic fields assuming the non-vanishing of a suitable Heegner point. Nekovar adapts Kolyvagin's method of Euler systems to the context of modular forms of even weight larger than 2. In my thesis, I consider the setting where the modular form is twisted by an unramified algebraic Hecke character of infinite type. In this talk, we discuss the key elements of Kolyvagin’s method of Euler systems applied to elliptic curves and modular forms.