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

Abstract

In this paper we study the analyticity of the group action of the automorphism group $G$ of a formal module $\bar{F}$ of height 2 (defined over ${\overline{\mathbb{F}}}_q$) on the Lubin-Tate deformation space $X$ of $\bar{F}$. It is shown that a wide open congruence group of level zero attached to a non-split torus acts analytically on a particular disc in $X$ on which the period morphism is not injective. For certain other discs with larger radii (defined in terms of quasi-canonical liftings) we find wide open rigid analytic groups which act analytically on these discs.

References in corpus (1)

• Domains of Injectivity for the Gross-Hopkins Period Map

Cited by in corpus (1)

• Locally analytic representations in the étale coverings of the Lubin-Tate moduli space