Rigid-analytic varieties with projective reduction violating Hodge symmetry

We construct examples of smooth proper rigid-analytic varieties admitting formal models with projective special fibers and violating Hodge symmetry for cohomology in degrees >= 3. This answers negatively the question raised by Hansen and Li.

Automated summary

The authors provide examples of smooth proper rigid-analytic varieties with formal models having projective special fibers that violate Hodge symmetry for cohomology in degrees >= 3, thereby giving a negative answer to a question posed by Hansen and Li.