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arXiv · 1711.06436

Cohomologically rigid local systems and integrality

Hélène Esnault·Michael Groechenig
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Abstract

We prove that the monodromy of an irreducible cohomologically complex rigid local system with finite determinant and quasi-unipotent local monodromies at infinity on a smooth quasiprojective complex variety $X$ is integral. This answers positively a special case of a conjecture by Carlos Simpson. On a smooth projective variety, the argument relies on Drinfeld's theorem on the existence of $\ell$-adic companions over a finite field. When the variety is quasiprojective, one has in addition to control the weights and the monodromy at infinity.

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Hélène Esnault, Michael Groechenig. 2017-11-17. Cohomologically rigid local systems and integrality. https://arxiv.org/abs/1711.06436

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