Domains of Injectivity for the Gross-Hopkins Period Map

TL;DR

This paper characterizes the injectivity domains of the Gross-Hopkins Period map for height 2 formal modules and explores the local analyticity of automorphism group actions on deformation spaces.

Contribution

It precisely determines the injectivity domain of the period map and applies this to establish local analyticity of automorphism group actions.

Findings

Identified the injectivity domain of the Gross-Hopkins Period map for height 2 modules.

Proved local analyticity of automorphism group actions on deformation spaces.

Enhanced understanding of the structure of deformation spaces in p-adic geometry.

Abstract

We determine the domain of injectivity of the Gross-Hopkins Period map around each points in the deformation space for a fixed formal module $\bar{F}$ of height 2 that defined over a finite field. And then we will use this to conclude some local analyticity result of the group action for the automorphism group of $\bar{F}$ on the deformation space.