Number Theory Seminar

I will first give an overview of the theory of Euler systems and its use in Iwasawa Theory. I will then review a recent work of Loeffler and Zerbes, who have defined certain cohomology classes for the Rankin-Selberg product of two Coleman families. I will explain a factorisation technique that can be used to turn these classes into a bounded Euler system for the Rankin-Selberg product of two modular forms with mixed reduction type. If time permits, I will discuss some applications in the Iwasawa theory of modular forms over imaginary quadratic fields. This is joint work with Kazim Buyukboduk.