Vanishing results for the Aomoto complex of real hyperplane arrangements via minimality

Abstract

We prove vanishing results of the cohomology groups of Aomoto complex over arbitrary coefficient ring for real hyperplane arrangements. The proof is using minimality of arrangements and descriptions of Aomoto complex in terms of chambers. Our methods also provide a new proof for the vanishing theorem of local system cohomology groups which was first proved by Cohen, Dimca and Orlik.