5 papers
Poincaré duality for pro-étale -local systems
Shizhang Li, Wiesława Nizioł, Emanuel Reinecke +1
We prove finiteness and Poincaré duality for pro-étale -local systems on proper -adic rigid-analytic spaces in the framework of Banach--Colmez spaces and establish…
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…
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…
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…
Algebraization Techniques and Rigid-Analytic Artin-Grothendieck Vanishing
Ofer Gabber, Bogdan Zavyalov
First, we prove an algebraization result for rig-smooth algebras over a general noetherian ring; this positively answers the question raised in [Sta24, Tag 0GAX]. Then we prove a g…