In analogy to Simpson's non-abelian Hodge correspondence over the complex numbers, p-adic non-abelian Hodge theory over non-archimedean fields aims to relate p-adic representations of the étale fundamental group of a smooth proper rigid space X to Higgs bundles on X. Conjecturally, this should lead to a "p-adic Simpson correspondence", whose precise formulation is however currently still mysterious. In this talk, I will first explain how the correspondence can be reinterpreted in terms of vector bundles on Scholze's pro-étale site. I will then introduce analytic moduli spaces for either side of the correspondence, and explain how these can be compared geometrically, resulting in a non-abelian generalisation of the Hodge--Tate exact sequence.
Freitag, den 6. Mai 2022 um 13:30 Uhr, in INF 205, SR A Freitag, den 6. Mai 2022 at 13:30, in INF 205, SR A
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Dr. Katharina Hübner