* No registration is required in advance. Interested participants may register on site.

In this lecture series, we will explain our construction (jointly with Hansheng Diao) of a tensor functor from the category of de Rham p-adic etale local systems, over a smooth algebraic variety over a p-adic local field, to the category of filtered algebraic vector bundles with integrable connections satisfying the Griffiths transversality, which we view as a p-adic analogue of Degline's classical Riemann-Hilbert correspondence.  Our construction is based on a rigid analytic construction with logarithmic poles along the boundary of suitable compactifications of the algebraic variety, which will be a main theme of our lectures.  As an application, we will also show that this p-adic Riemann-Hilbert functor is compatible with the classical one over all Shimura varieties, for local systems attached to representations of the associated reductive algebraic groups.

Our lectures will cover three major aspects: (i) foundations on p-adic geometry and log adic spaces; (ii) the log Riemann-Hilbert correspondences and comparison of cohomology; and (iii) applications to Shimura varieties.  A tentative plan (subject to change) is as follows:

On Monday:

     (1) Overview by Xinwen Zhu

     (2) Lecture one on p-adic geometry by Ruochuan Liu

     (3) Shimura varieties and their compactifications by Kai-Wen Lan

On Tuesday:

     (4) Lecture two on p-adic geometry by Ruochuan Liu

     (5) Log adic spaces by Xinwen Zhu

On Wednesday:

     (6) Period sheaves by Ruochuan Liu

     (7) Local systems over Shimura varieties by Kai-Wen Lan

On Thursday:

     (8) Decompletions by Ruochuan Liu

     (9) Coherence by Xinwen Zhu

     (10) Residues by Kai-Wen Lan

On Friday:

     (11) Comparison of cohomology by Xinwen Zhu

     (12) Compatibility with classical constructions over Shimura varieties by Kai-Wen Lan

INVITED SPEAKERS

     Kai-Wen Lan (University of Minnesota)

     Ruochuan Liu (BICMR)

     Xinwen Zhu (Caltech)

ORGANIZING COMMITTEE

     Minhyong Kim (Oxford/KIAS)

     Sug Woo Shin (UC Berkeley/KIAS)

CONTACT

     Da-eun Kim (dekim@kias.re.kr)