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Semiampleness for Calabi--Yau surfaces in positive and mixed characteristic
Fabio Bernasconi, Liam Stigant
In this note we prove the semiampleness conjecture for klt Calabi--Yau surface pairs over an excellent base ring. As applications we deduce that generalised abundance and Serrano's…
Abundance theorem for threefolds in mixed characteristic
Fabio Bernasconi, Iacopo Brivio, Liam Stigant
We show the abundance theorem for arithmetic klt threefold pairs whose closed point have residue characteristic greater than five. As a consequence, we give a sufficient condition…
Mori Fibrations in Mixed Characteristic
Liam Stigant
This paper resolves several outstanding questions regarding the Minimal Model Program for klt threefolds in mixed characteristic. Namely termination for pairs which are not pseudo-…
The Augmented Base Locus in Mixed Characteristic
Liam Stigant
Let be a nef and big line bundle on a scheme . It is well known that if is a projective over a field then the augmented base locus and the exceptional base locus agree.…
On the Boundedness of Globally -split varieties
Liam Stigant
This paper proposes the use of -split and globally -regular conditions in the pursuit of BAB type results in positive characteristic. The main technical work comes in the for…