Domains of Injectivity for the Gross-Hopkins Period Map

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.

This second version provides a totally different approach to the question. This theoretic approach uses arguments as in Lubin-Tate theory and relates the structure of the fiber of the Period map with quasi-isogenies. In the first version, the Newton's Polygon of the local Taylor series expansion is determined. And we add some local analyticity results to second version

Cited by in corpus (1)

• On the Analyticity of the group action on the Lubin-Tate space