8 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…
Adjoint test modules along Cohen--Macaulay morphisms
Javier Carvajal-Rojas, Axel Stäbler
We provide a transformation rule for adjoint test modules along Cohen--Macaulay maps between Cohen--Macaulay varieties that have -rational geometric fibers. This is, in part, an…
Pulling back Cartier structures along regular maps
Javier Carvajal-Rojas, Axel Stäbler
We introduce a framework for pulling back Cartier modules and their associated invariants along regular -finite morphisms. To achieve this, we construct a relative Cartier isomo…
On pristine morphisms
Javier Carvajal-Rojas, Axel Stäbler
We investigate flat morphisms of schemes of positive characteristic whose relative Frobenius is an isomorphism, which we call pristine. We show that these give rise to a natural Gr…
The geometry of Frobenius on toric varieties
Javier Carvajal-Rojas, Emre Alp Ãzavcı
We give a geometric description of the positivity of the Frobenius-trace kernel on a -factorial projective toric variety. To do so, we define its Frobenius support as w…
Varieties with ample Frobenius-trace kernel
Javier Carvajal-Rojas, Zsolt Patakfalvi
In the search of a projective analog of Kunz's theorem and a Frobenius-theoretic analog of Mori--Hartshorne's theorem, we investigate the positivity of the kernel of the Frobenius…