Dimension of the deformation space of ordinary representations in the cyclotomic limit

TL;DR

This paper investigates the deformation space of ordinary Galois representations in the cyclotomic limit, demonstrating that its dimension can be arbitrarily large under certain conditions.

Contribution

It proves that the ordinary deformation ring over the cyclotomic tower can have unbounded dimension, extending understanding of deformation spaces in number theory.

Findings

Weight two ordinary deformations are unobstructed in the cyclotomic limit.

The deformation ring's dimension can be arbitrarily large.

Results depend on specific assumptions in the cyclotomic setting.

Abstract

The weight two ordinary deformations are unobstructed in the cyclotomic limit under certain assumptions. We show that such an ordinary deformation ring over the cyclotomic tower can have arbitrarily large dimension.