The de Rham cohomology of Drinfeld's half space

TL;DR

This paper offers a new approach to computing the de Rham cohomology of Drinfeld's half space over a p-adic field, building on and providing an alternative to previous methods.

Contribution

It introduces a novel method for analyzing the de Rham complex of Drinfeld's half space using recent theoretical developments.

Findings

Explicit computation of de Rham cohomology for Drinfeld's half space

New proof technique based on recent results

Enhanced understanding of p-adic geometric invariants

Abstract

Let X 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 there were given different proofs by Alon, de Shalit, Iovita and Spiess. This paper presents yet another approach for the determination of these invariants by analysing the de Rham complex of X from the viewpoint of recent results by the author.