We show that mixed-characteristic and equicharacteristic small deformations of 3-dimensional canonical (resp., terminal) singularities with perfect residue field of characteristic p>5 are canonical (resp., terminal). We discuss applications to arithmetic a ...
We prove the abundance theorem for arithmetic klt threefold pairs whose closed point have residue characteristic greater than 5. As a consequence, we give a sufficient condition for the asymptotic invariance of plurigenera for certain families of singular ...
We prove Grauert-Riemenschneider-type vanishing theorems for excellent divisiorally log terminal threefolds pairs whose closed points have perfect residue fields of positive characteristic p > 5. Then we discuss applications to dlt singularities and to Mor ...
We prove the Kawamata-Viehweg vanishing theorem for surfaces of del Pezzo type over perfect fields of positive characteristic p > 5. As a consequence, we show that klt threefold singularities over a perfect base field of characteristic p > 5 are rational. ...
In this note, we prove the semiampleness conjecture for Kawamata log terminal Calabi-Yau (CY) surface pairs over an excellent base ring. As applications, we deduce that generalized abundance and Serrano's conjecture hold for surfaces. Finally, we study the ...
