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arXiv · 2607.14517

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

Alexander Petrov·Bogdan Zavyalov
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Abstract

We prove that \'etale 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. This is achieved by showing that the underlying $E_\infty$-algebra of a monodromy-pure $E_\infty$-algebra in Weil--Deligne representations is formal. We give examples of smooth proper rigid-analytic surfaces whose cohomology algebras are not formal.

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Alexander Petrov, Bogdan Zavyalov. 2026-07-16. Formality for rigid-analytic spaces satisfying the weight-monodromy conjecture. https://arxiv.org/abs/2607.14517

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