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The \(l\)-adic cohomology of hyperplane complements. (English) Zbl 0770.14013

The cohomology ring of a complement of a union of hyperplanes in \(\mathbb{C}^ r\) with integral equations was studied by Brieskorn, Arnold and Orlik-Solomon. In this paper one gives similar results for the \(\ell\)- adic cohomology of the analogous variety over the algebraic closure of the prime field \(\mathbb{F}_ p\).

MSC:

14F30 \(p\)-adic cohomology, crystalline cohomology
14F45 Topological properties in algebraic geometry
20G40 Linear algebraic groups over finite fields
57S25 Groups acting on specific manifolds
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