Higher Hida theory for Hilbert modular varieties.

The general goal of Higher Hida theory is to define and understand the ordinary part of integral coherent cohomology of Shimura varieties. In this talk we will focus on the simplest example of a Shimura variety for a non-split reductive group. We describe the results, notably vanishing theorems and Jacquet-Langlands isomorphisms.  Joint work with G. Boxer.