ON THE CONNECTED COMPONENTS OF MODULI SPACES OF FINITE FLAT MODELS

• Published in: American journal of mathematics Vol. 132; no. 5; pp. 1189 - 1204
• Main Author: Imai, Naoki
• Format: Journal Article
• Language: English
• Published: Baltimore, MD Johns Hopkins University Press 01.10.2010
• Subjects: Algebra; Conceptual lattices; Exact sciences and technology; General mathematics; General, history and biography; Inertia; Integers; Mathematical models; Mathematical notation; Mathematical rings; Mathematical theorems; Mathematics; Modularity; Number theory; Sciences and techniques of general use; Theorems; Theoretical mathematics; Finite field; Deformation; Ring; Moduli space; Connected space; Two dimensional model; Representation

We prove that the nonordinary component is connected in the moduli spaces of finite flat models of two-dimensional local Galois representations over finite fields. This was conjectured by Kisin. As an application to global Galois representations, we prove a theorem on the modularity comparing a defo...