Cohomologically rigid local systems and integrality

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...

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Bibliographic Details
Published in:Selecta mathematica (Basel, Switzerland) Switzerland), 2018-11, Vol.24 (5), p.4279-4292
Main Authors: Esnault, Hélène, Groechenig, Michael
Format: Article
Language:English
Subjects:
Existence theorems
Infinity
Mathematics
Mathematics and Statistics
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Summary: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 ℓ -adic companions over a finite field. When the variety is quasiprojective, one has in addition to control the weights and the monodromy at infinity.
ISSN:1022-1824
1420-9020
DOI:10.1007/s00029-018-0409-z