Kawamata-Viehweg Vanishing Theorem for del Pezzo Surfaces over imperfect fields in characteristic $p>3$

TL;DR

This paper proves that the Kawamata-Viehweg vanishing theorem applies to regular del Pezzo surfaces over imperfect fields in characteristic greater than 3, extending its validity in algebraic geometry.

Contribution

It establishes the Kawamata-Viehweg vanishing theorem for a new class of surfaces over imperfect fields in characteristic p>3, which was previously unknown.

Findings

Vanishing theorem holds for regular del Pezzo surfaces over imperfect fields in characteristic p>3

Extends the applicability of the Kawamata-Viehweg theorem in algebraic geometry

Provides new insights into the behavior of algebraic surfaces in positive characteristic

Abstract

In this article we prove that the Kawamata-Viehweg vanishing theorem holds for regular del Pezzo surfaces over imperfect ground fields of characteristic $p>3$.