The Orlik–Solomon complex and Milnor fibre homology

Fix a real hyperplane arrangement, and let F be the Milnor fibre of its complexified defining polynomial. We consider a filtration of the homology of F that arises from the algebraic monodromy, using integer or Z/pZ coefficients. We compare it with the cohomology of the Orlik–Solomon algebra, over Z or Z/pZ, respectively, with respect to a suitable “Koszul” boundary map, and find isomorphisms in certain cases. This continues work by various authors in comparing the cohomology of certain local systems on a hyperplane complement with that of the Orlik–Solomon algebra.