3 papers
math.AG2026
Cohomological flatness over discrete valuation rings: numerical and logarithmic criteria
Ofer Gabber, Rémi Lodh
We give sufficient conditions for cohomological flatness (in dimension 0) over discrete valuation rings, generalizing classical results of Raynaud in two different ways. The first…
math.AG2025
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…
math.AG2025
Bounding crystalline torsion from étale torsion
Ofer Gabber, Shizhang Li
In this note, we prove that given a smooth proper family over a -adic ring of integers, one gets a control of its crystalline torsion in terms of its étale torsion, the cohomol…