3 citations · 8 across the 9 of their papers we have counts for
9 papers · 1 filter
Poincaré Duality in abstract 6-functor formalisms
Bogdan Zavyalov
We study Poincaré Duality in the context of abstract 6-functor formalisms. In particular, we give a small and simple list of assumptions that implies Poincaré Duality. As an applic…
Arithmetic Properties Of -adic Étale Cohomology and Nearby Cycles of Rigid-Analytic Spaces
David Hansen, Bogdan Zavyalov
We prove a number of results on the étale cohomology of rigid analytic varieties over -adic non-archimedean local fields. Among other things, we establish bounds for Frobenius e…
Lefschetz theorems in flat cohomology and applications
Sean Cotner, Bogdan Zavyalov
We prove a version of the Lefschetz hyperplane theorem for fppf cohomology with coefficients in any finite commutative group scheme over the ground field. As consequences, we estab…
Mod-p Poincaré Duality in p-adic Analytic Geometry
Bogdan Zavyalov
We show Poincaré Duality for -étale cohomology of a smooth proper rigid-analytic space over a non-archimedean field of mixed characteristic . It positivel…
Almost coherent modules and almost coherent sheaves
Bogdan Zavyalov
We review the theory of almost coherent modules that was introduced in "Almost Ring Theory" by Gabber and Ramero. Then we globalize it by developing a new theory of almost coherent…
Altered Local Uniformization Of Rigid-Analytic Spaces
Bogdan Zavyalov
We prove a version of Temkin's local altered uniformization theorem. We show that for any rig-smooth, quasi-compact and quasi-separated admissible formal -model $\ma…
Sheafiness of Strongy Rigid-Noetherian Huber Pairs
Bogdan Zavyalov
We show that any strongly rigid-noetherian Huber ring is sheafy. In particular, we positively answer Problem~ in the Nonarchimedean Scottish Book.
Quotients Of Admissible Formal Schemes and Adic Spaces by Finite Groups
Bogdan Zavyalov
In this paper we give a self-contained treatment of finite group quotients of admissible (formal) schemes and adic spaces that are locally topologically finite type over a locally…
Chow Groups of Abelian Varieties and Beilinson's Conjecture
Bogdan Zavyalov
In the present paper we introduce the property AA of a subsemigroup of the endomorphism semigroup of an abelian variety, which holds for semigroup of endomorphisms of an abelian va…