Integral Iwasawa theory of galois representations for non-ordinary primes

Modularity lifting theorems for ordinary Galois representations

We generalize the results of [CHT08] and [Tay08] by proving modularity lifting theorems for ordinary l-adic Galois representations of any dimension of a CM or totally real number field F . The main theorems are obtained by establishing an R = T theorem over a Hida family. A key part of the proof is to construct appropriate ordinary lifting rings at the primes dividing l and to determine their i...

Iwasawa theory for deformation of ordinary elliptic curves

Non-Ordinary Primes: A Story

This research was supported in part by grant DMS from the National Science Foundation A normalized modular eigenform f is said to be ordinary at a prime p if p does not divide the p-th Fourier coefficient of f. We take f to be a modular form of level 1 and weight k f12, 16, 18, 20, 22, 26g and search for primes where f is not ordinary. To do this, we need an efficient way to compute the reducti...

Deformation of Outer Representations of Galois Group

To a hyperbolic smooth curve defined over a number-field one naturally associates an "anabelian" representation of the absolute Galois group of the base field landing in outer automorphism group of the algebraic fundamental group. In this paper, we introduce several deformation problems for Lie-algebra versions of the above representation and show that, this way we get a richer structure than t...

Galois modules, Iwasawa theory and leading term conjectures