Control of Λ-adic mordell–weil groups

Abstract

The (pro) Λ-MW group is a projective limit of Mordell–Weil groups over a number field k (made out of modular Jacobians) with an action of the Iwasawa algebra and the “big” Hecke algebra. We prove a control theorem of the ordinary part of the Λ-MW groups under mild assumptions. We have proven a similar control theorem for the dual completed inductive limit in [21].