Corpus ID: 237635017

Cohomology of semisimple local systems and the Decomposition theorem

  title={Cohomology of semisimple local systems and the Decomposition theorem},
  author={Chuanhao Wei and Ruijie Yang},
  • Chuanhao Wei, Ruijie Yang
  • Published 23 September 2021
  • Mathematics
In this paper, we study the cohomology of semisimple local systems in the spirit of classical Hodge theory. On the one hand, we establish a generalization of Hodge-Riemann bilinear relations. For a semisimple local system on a smooth projective variety, we define a canonical isomorphism from the complex conjugate of its cohomology to the cohomology of the dual local system, which is a generalization of the classical Weil operator for pure Hodge structures. This isomorphism establishes a… Expand


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