p-adic Hodge Theory, Deformations of Galois Representations, and p-divisible groups

The point of this seminar is to learn the foundations of p-adic Hodge theory and its application to p-divisible groups. The goal is to understand Kisin's recent paper

"Moduli of Finite Group Schemes, and Modularity" in the Annals of Mathematics. In this paper, Kisin uses p-adic Hodge theory as well as the theory of Mazur, Wiles, and others of deforming galois representations. Kisin shows that Galois representations attached to certain 2-dimensional p-divisible groups are modular. One application is a proof of the

modularity theorem (Taniyama-Shimura conjecture). Some references:

Expository notes by Brian Conrad: http://math.stanford.edu/~conrad/papers/notes.pdf

Kisin's paper: http://annals.math.princeton.edu/wp-content/uploads/annals-v170-n3-p03-p.pdf

Fontaines book on p-divisible groups over local rings and Honda systems: Groupes p-divisibles sur les corps locaux

Tate's expository article "Finite Flat Group Schemes"

Tate's research article "p-divisible groups"

Barry Mazur: "Introduction to the Deformations of Galois Representations"

Haruzo Hida's book "Modular Forms and Galois Cohomology"

Schedule of Talks: