Pro-étale vector bundles and the p-adic Simpson correspondence

Abstract: I will first explain how various classical problems in p-adic number theory such as Sen theory can be reinterpreted geometrically in terms of vector bundles on Scholze's pro-étale site. I will then explain how such pro-étale vector bundles can be understood systematically by means of "p-adic non-abelian Hodge theory". This is closely related to Faltings' p-adic Simpson correspondence, relating p-adic representations of fundamental groups of p-adic varieties to Higgs bundles. Finally, I will sketch how moduli spaces of pro-étale vector bundles can help understand open questions in Sen theory and the p-adic Simpson correspondence.

number theory

Audience: researchers in the topic

London number theory seminar

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