Seminar in Algebraic Geometry and Number Theory

Abstract: In this lecture I will discuss several variants of a conjecture of Darmon, Lauder and myself. 

Given a triple (f, g, h) of modular forms of weights (2, 1, 1), the conjecture formulates a p-adic BSD-type relationship 

between an analytic iterated integral and a regulator given by logarithms of global points. I will focus on the particularly
intriguing case where the weight one form g gives rise to a point on the eigencurve that
fails to be étale over weight space.