Banach space representations and Iwasawa theory

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.

Non-smooth Analysis, Optimisation Theory and Banach Space Theory

The questions listed here do not necessarily represent the most significant problems from the areas of Non-smooth Analysis, Optimisation theory and Banach space theory, but rather, they represent a selection of problems that are of interest to the authors. 1. Weak Asplund spaces Let X be a Banach space. We say that a function φ : X → R is Gâteaux differentiable at x ∈ X if there exists a contin...

Introduction to Iwasawa Theory

Coorbit Space Theory for Quasi-Banach Spaces

We generalize the classical coorbit space theory developed by Feichtinger and Gröchenig to quasi-Banach spaces. As a main result we provide atomic decompositions for coorbit spaces defined with respect to quasi-Banach spaces. These atomic decompositions are used to prove fast convergence rates of best n-term approximation schemes. We apply the abstract theory to time-frequency analysis of modul...

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.