Combinatorial covers and vanishing of cohomology

• Graham Denham ^[1] ; Alexander I. Suciu ^[2] ; Sergey Yuzvinsky ^[3]
  1. [1] University of Western Ontario

     University of Western Ontario

     Canadá

     
  2. [2] Northeastern University
  3. [3] University of Oregon

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 22, Nº. 2, 2016, págs. 561-594
• Idioma: inglés
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• Resumen

  • 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.