Note on weight-monodromy conjecture for p-adically uniformized varieties

TL;DR

This paper proves the weight-monodromy conjecture for p-adically uniformized varieties using existing work on the cohomology of Drinfeld upper half spaces, advancing understanding in p-adic geometry.

Contribution

It establishes the conjecture for a new class of varieties, leveraging Dat's results on the cohomology complex of Drinfeld upper half spaces.

Findings

Proves the weight-monodromy conjecture for p-adically uniformized varieties.

Connects the conjecture to Dat's work on cohomology complexes.

Simplifies the proof by building on existing cohomology results.

Abstract

We prove the weight-monodromy conjecture for varieties which are p-adically uniformized by a product of the Drinfeld upper half spaces. It is an easy consequence of Dat's work on the cohomology complex of the Drinfeld upper half space.