A p-adic Simpson correspondence for smooth proper rigid varieties

2023/07/03 by Heuer, Ben · 2 citations
#14D22 #14G22 #14G45 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.01303

Abstract

For any smooth proper rigid analytic space X over a complete algebraically closed extension of \mathbb Q_p, we construct a p-adic Simpson correspondence: an equivalence of categories between vector bundles on Scholze's pro-étale site of X and Higgs bundles on 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.

Cited by

• A p-adic Simpson correspondence for singular rigid-analytic varieties
• A remark on the vanishing of Higgs fields in the p-adic Simpson correspondence

Related

• Rigid analytic p-adic Simpson correspondence for line bundles
• A geometric p-adic Simpson correspondence in rank one
• Moduli spaces in p-adic non-abelian Hodge theory
• The small p-adic Simpson correspondence in terms of moduli spaces
• A note on p-adic Simpson correspondence