Rigid analytic p-adic Simpson correspondence for line bundles

TL;DR

This paper extends Faltings' p-adic Simpson correspondence for line bundles to a rigid analytic morphism of moduli spaces, under certain conditions, paralleling complex non-abelian Hodge theory.

Contribution

It provides a p-adic analogue of Simpson's complex analytic morphism, enhancing the p-adic Simpson correspondence to a geometric morphism between moduli spaces.

Findings

Established a rigid analytic morphism for line bundles in p-adic setting.

Extended the p-adic Simpson correspondence to a geometric morphism.

Under certain smallness conditions, the correspondence becomes a morphism of moduli spaces.

Abstract

The p-adic Simpson correspondence due to Faltings 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.