What question did this study set out to answer?

The research aims to establish connections between moduli stacks and p-adic Hodge theory for curves.

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December 9, 2025

𝑝-Adic non-abelian Hodge theory for curves via moduli stacks

Key Points

The research aims to establish connections between moduli stacks and p-adic Hodge theory for curves.
Analyzes moduli stack of G-Higgs bundles on a smooth projective curve
Investigates geometric properties via twists of moduli stacks
Explores the Faltings correspondence and connections to p-adic representations
Demonstrates a homeomorphism between points of moduli spaces
Connects stack of p-adic representations of π1(X) to semi-stable Higgs bundles
Shows a canonical twist of moduli stacks enhances understanding of Higgs bundles

Abstract

For a smooth projective curve X X over C p Cₚ and any reductive group G G, we show that the moduli stack of G G -Higgs bundles on X X is a twist of the moduli stack of v-topological G G -bundles on X v Xᵥ in a canonical way. We explain how a choice of an exponential trivialises this twist on points. This yields a geometrisation of Faltings’ p p -adic Simpson correspondence for X X, which we recover as a homeomorphism between the points of moduli spaces. We also show that our twisted isomorphism sends the stack of p p -adic representations of π 1 (X) ₁ (X) to an open substack of the stack of semi-stable Higgs bundles of degree 0 0.

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