A p-adic Simpson correspondence for smooth proper rigid varieties

• 成果类型: Article
• 署名作者: Heuer, Ben
• 署名单位: Goethe University Frankfurt
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-025-01321-4
• 发表日期: 2025
• 页码: 261-312
• 关键词: bundles

摘要

For any smooth proper rigid analytic space X over a complete algebraically closed extension of Qp, we construct a p-adic Simpson correspondence: an equivalence of categories between vector bundles on Scholze's pro-etale 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-etale invertible sheaves on spectral varieties.