On exceptional rigid local systems
نویسنده
چکیده
Let G be a reductive algebraic group over C and let X be a smooth quasiprojective complex variety. Let us call a representation ρ : π1(X) → G to be G-rigid, if the set theoretic orbit of the representation ρ in the representation space Hom(π1(X), G) under the action of G is an open subset. Note that by fixing an embedding of G into a general linear group GLn(C), any representation ρ : π1(X) → G corresponds uniquely to a local system Lρ on X, see [3]. On the other hand, any local system on X whose monodromy lies in G ≤ GLn gives rise to a representation ρ = ρL : π1(X) → G. The local system L = Lρ is called G-rigid, if ρ is G-rigid. A local system is called quasi-unipotent, if the eigenvalues of the local monodromies of L are roots of unity. The following conjecture is motivated by Hodge theory and appears in work of Simpson [10] (for projective X):
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