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.