Pseudo-modularity and Iwasawa theory

Pseudo-modularity and Iwasawa Theory

We prove, assuming Greenberg’s conjecture, that the ordinary eigencurve is Gorenstein at an intersection point between the Eisenstein family and the cuspidal locus. As a corollary, we obtain new results on Sharifi’s conjecture. This result is achieved by constructing a universal ordinary pseudodeformation ring and proving an R = T result.

Iwasawa theory and generalizations

This is an introduction to Iwasawa theory and its generalizations. We discuss some main conjectures and related subjects. Mathematics Subject Classification (2000). Primary 11R23; Secondary 11G40, 14G10.

Introduction to Iwasawa Theory

Iwasawa Theory for Elliptic Curves

The topics that we will discuss have their origin in Mazur’s synthesis of the theory of elliptic curves and Iwasawa’s theory of ZZp-extensions in the early 1970s. We first recall some results from Iwasawa’s theory. Suppose that F is a finite extension of Q and that F∞ is a Galois extension of F such that Gal(F∞/F ) ∼= ZZp, the additive group of p-adic integers, where p is any prime. Equivalentl...

Ben Rosenfield Iwasawa-Tate Theory

This will contain my notes on Iwasawa-Tate theory. This will be done first for number fields and simple algebras (a la Weil), giving some number theoretic results. The meat of these notes is a study of the Standard L-functions for GL(n). We extend this to arbitary simple algebras (a la Godement/Jacquet). This is a long term project. As of now, I have basically completed the first case. There ar...