Control Theorem for Greenbergʹs Selmer Groups of Galois Deformations Original Research Article

We give sufficient conditions for the Selmer group of a p-adic deformation of a motive over a number field to be controlled. Then we apply this result to the Selmer groups of various Galois representations. For example, we treat the cyclotomic deformations and the Hida deformations of the representations associated to modular forms.