# Cohomology of semisimple local systems and the Decomposition theorem

@inproceedings{Wei2021CohomologyOS, title={Cohomology of semisimple local systems and the Decomposition theorem}, author={Chuanhao Wei and Ruijie Yang}, year={2021} }

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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