Number Theory Seminar

I will explain a definition of Euler systems for anticyclotomic extensions of a CM extension K/F. This allows one to prove analogs of Kolyvagin's famous results for Heegner points (rank one, finiteness of Tate-Shafarevich groups) for a very general class of Galois representations over CM fields. A novel feature of this approach is to focus on primes that split in K/F (as opposed to Kolyvagin's inert primes). I will also describe some of the many examples of such Euler systems that have been constructed recently. This is joint work with Dimitar Jetchev and was begun in collaboration with Jan Nekovar.