Work

A $p$-adic Simpson correspondence for smooth proper rigid varieties

Year: 2025

Type: article

Abstract: For any smooth proper rigid analytic space $X$ X over a complete algebraically closed extension of $\mathbb{Q}_{p}$ Q p , we construct a $p$ p -adic Simpson correspondence: an equivalence of categories between vector bundles on Scholze’s pro-étale site of $X$ X and Higgs bundles on $X$ X . This generalises a result of Faltings from smooth projective curves to any higher dimension, and further to the rigid analytic setup. The strategy is new, and is based on the study of rigid analytic moduli spaces of pro-étale invertible sheaves on spectral varieties.

Source: Inventiones mathematicae

DOI: 10.1007/s00222-025-01321-4

Author: Ben Heuer

Institution: Goethe University Frankfurt

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: Deutsche Forschungsgemeinschaft