Λ-adic Kolyvagin Systems

Abstract

In this paper we study Kolyvagin Systems, as defined by Mazur and Rubin, over the cyclotomic Zp-tower for a Gal(Q=Q) representation T. We prove, under certain hypotheses, that the module of -adic Kolyvagin Systems for the cyclotomic deformation T is free of rank one over the cyclotomic Iwasawa algebra. We link our result with a web of conjectures due to Perrin-Riou and Rubin; and we relate the -adic Kolyvagin Systems we prove to exist to (conjectural) p-adic L-functions. We also study the Iwasawa theory of Rubin-Stark elements via the perspective offered by our main theorem, and outline a strategy to deduce the main conjectures of Iwasawa theory for totally real number fields assuming the Rubin-Stark conjecture.