I have done some research about -adic symmetric spaces in my master’s thesis. More precisely, I prove a Hodge-type decomposition for the de Rham cohomology of
-adically uniformized varieties by the product of
-adic symmetric spaces. It is based on work of Schneider, Stuhler, Iovita and Spiess on cohomology of
-adic symmetric space.
- Hodge-type decomposition for de Rham cohomology of
-adically uniformized Varieties, preprint 2018. https://arxiv.org/abs/1811.01153