Jonathan Pottharst (Boston College)

Selmer groups over eigenvarieties

Abstract: Greenberg defined Selmer groups over p-adic deformations of motives that are "ordinary". This leaves open the question of how to define a Selmer group over, for example, the eigencurve of Coleman-- Mazur. We present a conjectural program to do this, using a direct generalization of Greenberg's hypothesis in the setting of (phi,Gamma)- modules, and give evidence by comparing our local conditions to Bloch-- Kato's.