Combinatorial covers and vanishing of cohomology
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- Denham, G., Suciu, A.I. & Yuzvinsky, S. Sel. Math. New Ser. (2016) 22: 561. doi:10.1007/s00029-015-0196-8
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We use a Mayer–Vietoris-like spectral sequence to establish vanishing results for the cohomology of complements of linear and elliptic hyperplane arrangements, as part of a more general framework involving duality and abelian duality properties of spaces and groups. In the process, we consider cohomology of local systems with a general, Cohen–Macaulay-type condition. As a result, we recover known vanishing theorems for rank-1 local systems as well as group ring coefficients and obtain new generalizations.