G-rigid local systems are integral
| Autor: | Klevdal, Christian, Patrikis, Stefan |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let $G$ be a reductive group, and let $X$ be a smooth quasi-projective complex variety. We prove that any $G$-irreducible, $G$-cohomologically rigid local system on $X$ with finite order abelianization and quasi-unipotent local monodromies is integral. This generalizes work of Esnault and Groechenig when $G= \mathrm{GL}_n$, and it answers positively a conjecture of Simpson for $G$-cohomologically rigid local systems. Along the way we show that the connected component of the Zariski-closure of the monodromy group of any such local system is semisimple. Comment: 21 pages |
| Databáze: | arXiv |
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