Abstract:

I will give an overview of the construction of a Riemann-Hilbert functor for p-adic etale local systems over smooth algebraic varieties, which can be viewed as a p-adic analogue of Deligne's classical Riemann-Hilbert correspondence for local systems over smooth algebraic varieties over the complex numbers, by establishing a logarithmic Riemann-Hilbert functor over proper smooth rigid analytic varieties.  If time permits, I will try to highlight certain special phenomena which are not obvious from the outset.  (This is based on joint work with Hansheng Diao, Ruochuan Liu, and Xinwen Zhu.)