[ 2018 KIAS CMC Thematic Program - 1 ]



KIAS Intensive Lecture Series:


Logarithmic Riemann-Hilbert correspondences


for rigid varieties and applications to Shimura varieties


August 6-10, 2018                                  KIAS 1503


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* 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




     Kai-Wen Lan (University of Minnesota)

     Ruochuan Liu (BICMR)

     Xinwen Zhu (Caltech)




     Minhyong Kim (Oxford/KIAS)

     Sug Woo Shin (UC Berkeley/KIAS)




     Da-eun Kim (dekim@kias.re.kr)