We prove several asymptotic vanishing theorems for Frobenius twists of ample vector bundles in positive characteristic. As an application, we improve the Bott-Danilov-Steenbrink vanishing theorem for ample vector bundles on toric varieties.
"Vanishing for Frobenius twists of ample vector bundles." Tohoku Math. J. (2) 71 (4) 549 - 557, 2019. https://doi.org/10.2748/tmj/1576724793