The de Rham cohomology of Drinfeld's halfspace

Abstract:  Let $X \subset \mathbb{P}_K^d$ be Drinfeld's  half space over a $p$-adic field $K$. The de Rham cohomology of $X$ was first computed by Schneider and Stuhler. Afterwards different proofs were given by Alon, de Shalit, Iovita and Spiess. In my talk I explain yet another approach for the determination of these invariants by analysing the Rham complex.