# Vanishing for Frobenius Twists of Ample Vector Bundles

## TL;DR

This paper establishes asymptotic vanishing theorems for Frobenius twists of ample vector bundles in positive characteristic and generalizes classical vanishing results to toric varieties.

## Contribution

It introduces new asymptotic vanishing theorems for Frobenius twists of ample vector bundles and extends the Bott-Danilov-Steenbrink vanishing theorem to toric varieties.

## Key findings

- Proved asymptotic vanishing theorems for Frobenius twists in positive characteristic.
- Generalized the Bott-Danilov-Steenbrink vanishing theorem for toric varieties.
- Established conditions under which cohomology groups vanish asymptotically.

## Abstract

We prove several asymptotic vanishing theorems for Frobenius twists of ample vector bundles in positive characteristic. As an application, we prove a generalization of the Bott-Danilov-Steenbrink vanishing theorem for ample vector bundles on toric varieties.