3 papers
math.AG2026
Formality for rigid-analytic spaces satisfying the weight-monodromy conjecture
Alexander Petrov, Bogdan Zavyalov
We prove that étale and de Rham cohomology algebras of a smooth proper rigid-analytic space over a finite extension of are formal if the rigid-analytic space satisfi…
math.AG2024
Relative Poincaré duality in nonarchimedean geometry
Shizhang Li, Emanuel Reinecke, Bogdan Zavyalov
We prove a conjecture of Bhatt-Hansen that derived pushforwards along proper morphisms of rigid-analytic spaces commute with Verdier duality on Zariski-constructible complexes. In…
math.AG2024
Some Foundational Results In Adic Geometry
Bogdan Zavyalov
In this paper, we record some foundational results on adic geometry that seem to be missing in the existing literature. Namely, we develop the Proj construction and a theory of lci…