Computational Arithmetic Geometry Seminar

Let f be a modular eigenform, and V_f the associated representation of the absolute Galois group of Q. I will explain a result which says that V_f does not admit any first order deformations which arise from geometry. This is a special case of the conjectures of Deligne and Beilinson which relate extensions of motives and special values of L-functions.

I will explain the philosophy and motivation underlying this result, and give an application to universal deformation rings of Galois representations.