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- W3203267485 abstract "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 relation between the twisted Poincar'e pairing, a purely topological object, and a positive definite Hermitian pairing. On the other hand, we prove a global invariant cycle theorem for semisimple local systems. As an application, we give a new and geometric proof of Sabbah's Decomposition Theorem for the direct images of semisimple local systems under proper algebraic maps, without using the category of polarizable twistor D-modules." @default.
- W3203267485 created "2021-10-11" @default.
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- W3203267485 date "2021-09-23" @default.
- W3203267485 modified "2023-10-14" @default.
- W3203267485 title "Cohomology of semisimple local systems and the Decomposition theorem" @default.
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- W3203267485 doi "https://doi.org/10.48550/arxiv.2109.11578" @default.
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