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

Alexander Petrov; Bogdan Zavyalov

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

Algebraic Geometry 2026-07-16 v1 Number Theory

Authors: Alexander Petrov , Bogdan Zavyalov

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

Cite

@article{arxiv.2607.14517,
  title  = {Formality for rigid-analytic spaces satisfying the weight-monodromy conjecture},
  author = {Alexander Petrov and Bogdan Zavyalov},
  journal= {arXiv preprint arXiv:2607.14517},
  year   = {2026}
}

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