Dual complex of log Fano pairs and its application to Witt vector cohomology

TL;DR

This paper proves the contractibility of dual complexes for weak log Fano pairs and applies this to derive vanishing theorems for Witt vector cohomology and a rational point formula in three dimensions.

Contribution

It establishes the contractibility of dual complexes for weak log Fano pairs and applies this to new vanishing theorems and rational point formulas.

Findings

Dual complexes of weak log Fano pairs are contractible.

Derived a vanishing theorem for Witt vector cohomology.

Established a rational point formula in dimension three.

Abstract

We prove the contractibility of the dual complexes of weak log Fano pairs. As applications, we obtain a vanishing theorem of Witt vector cohomology of Ambro-Fujino type and a rational point formula in dimension three.