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

2026/07/16 by Alexander Petrov, Bogdan Zavyalov
#math.AG #math.NT

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Abstract

We prove that étale and de Rham cohomology algebras of a smooth proper rigid-analytic space over a finite extension of 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.

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