Comparison on p-adic Simpson correspondence and p-adic Riemann-Hilbert correspondence

Abstract: In 2005, Faltings constructed an equivalence between the category of Higgs bundles and that of generalized representations of the \'etale fundamental group for curves over a p-adic field. In 2013, Scholze introduced a fully faithful functor from the category filtered de Rham bundles to that of $\mathbb B_{dR}^+$-local systems. In this talk, I will show that for a filtered de Rham bundle the first graded piece of the $\mathbb B_{dR}^+$-local systems is just the generalized representation attached to its graded Higgs bundle. This is a joint work with Kang Zuo.

Mathematics

Audience: researchers in the topic

ICCM 2020