7 papers
When is Frobenius epic?
Javier Carvajal-Rojas, Rankeya Datta, Noah Olander +1
We prove that a homomorphism of rings of prime characteristic is b-nil formally unramified if and only if its relative Frobenius is an epimorphism. We specialize this result under…
A characteristic analog of formal lifting properties
Rankeya Datta, Noah Olander
A field extension of characteristic is formally étale if and only if the relative Frobenius of is an isomorphism. Inspired by this classical result, we explore…
-intersection flatness of dagger and Berkovich Tate algebras
Rankeya Datta, Jack J Garzella, Kevin Tucker
We show, using the techniques developed in arXiv:2504.06444 and arXiv:2305.11139, that dagger algebras and Tate algebras in the sense of Berkovich in prime characteristic h…
Variants on Frobenius Intersection Flatness and Applications to Tate Algebras
Rankeya Datta, Neil Epstein, Karl Schwede +1
The theory of singularities defined by Frobenius has been extensively developed for -finite rings and for rings that are essentially of finite type over excellent local rings. H…
Test ideals in mixed characteristic: a unified theory up to perturbation
Bhargav Bhatt, Linquan Ma, Zsolt Patakfalvi +5
Let be an integral scheme of finite type over a complete DVR of mixed characteristic. We provide a definition of a test ideal which agrees with the multiplier ideal after inver…
Mittag-Leffler modules and variants on intersection flatness
Rankeya Datta, Neil Epstein, Kevin Tucker
We systematically study the intersection flatness and Ohm-Rush properties for modules over a commutative ring, drawing inspiration from the work of Ohm and Rush and of Hochster and…