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  1. ; ; (, Inventiones mathematicae)
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  2. ; (, Transactions of the American Mathematical Society)
    Let G G be a reductive group, and let X X be a smooth quasi-projective complex variety. We prove that any G G -irreducible, G G -cohomologically rigid local system on X X with finite order abelianization and quasi-unipotent local monodromies is integral. This generalizes work of Esnault and Groechenig [Selecta Math. (N. S. ) 24 (2018), pp. 4279–4292; Acta Math. 225 (2020), pp. 103–158] when G = G L n G= \mathrm {GL}_n , and it answers positively a conjecture of Simpson [Inst. Hautes Études Sci. Publ. Math. 75 (1992), pp. 5–95; Inst. Hautes Études Sci. Publ. Math. 80 (1994), pp. 5–79] for G 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; this moreover holds when we relax cohomological rigidity to rigidity. 
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  3. ; ; (, Pacific Journal of Mathematics)
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  4. ; ; (, Duke Mathematical Journal)
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