Integral canonical models of Shimura varieties and the Tate conjecture for K3 surfaces in positive characteristic

Prof. Dr. Viehmann, Prof. Dr. Liedtke, S. Neupert

 

Time and Place

Content

This seminar has two goals: First of all we want to understand M. Kisin's construction of canonical integral models of Shimura varieties. For a long time this was only known in the case of PEL-type Shimura varieties, there due to Kottwitz's interpretation as a moduli space of abelian varieties (with additional structures). Recently a method was found to reduce the construction of integral models for Shimura varieties of abelian type first to ones of Hodge type and then further to the PEL-case.

In the second half we want to understand K. Madapusi Pera's proof of the Tate conjecture for K3 surfaces in positive (odd) characteristic. Our main focus will be to understand, how the newly constructed canonical integral models of Shimura varieties allow for the Kuga-Satake construction to be extended to odd characteristic and its properties to be controlled.

During the first meeting (and after a brief introduction to Shimura varieties over the complex numbers), an overview over the remaining talks is given and they are distributed.

Program

available here as a download.

Literature (Excerpt)