The Leray model of a matroid

We construct a combinatorial abstraction of the Leray spectral sequence associated with the De Concini—Procesi compactification of a complex hyperplane arrangement complement. We show that its homological properties generalise the ones that we expect from topology in the realizable case. Geometric and Hodge-theoretic arguments are replaced by combinatorial blowups, Groebner bases, and sheaves on posets.