Formality for rigid-analytic spaces satisfying the weight-monodromy conjecture

We prove that étale and de Rham cohomology algebras of a smooth proper rigid-analytic space over a finite extension of $\mathbf{Q}_p$ are formal if the rigid-analytic space satisfies the weight-monodromy conjecture.

We give examples of smooth proper rigid-analytic surfaces whose cohomology algebras are not formal.