Kolyvagin systems over the Iwasawa algebra and trivial zeros

In this talk, I will discuss the existence of lifts of Kolyvagin Systems for a p-adic representation T (free of finite rank over Z_p) of the absolute Galois group of the rationals, to a Kolyvagin System over the whole Iwasawa tower. This problem turns out to be related to the trivial zero phenomenon of p-adic L-functions.