Rigid Analytic p-Adic Simpson Correspondence for Line Bundles

Abstract

The p-adic Simpson correspondence due to Faltings (Adv Math 198(2):847–862, 2005) is a p-adic analogue of non-abelian Hodge theory. The following is the main result of this article: The correspondence for line bundles can be enhanced to a rigid analytic morphism of moduli spaces under certain smallness conditions. In the complex setting, Simpson shows that there is a complex analytic morphism from the moduli space for the vector bundles with integrable connection to the moduli space of representations of a finitely generated group as algebraic varieties. We give a p-adic analogue of Simpson’s result.