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Title:
Integrality of the Betti Moduli Space
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Abstract:
Let X be a smooth projective variety over the complex numbers. Let M be the moduli space of irreducible representations of the topological fundamental group of X of a fixed rank r. Then M is a finite type scheme over the spectrum of the integers Z. One may ask if the irreducible components of M surject onto Spec(Z) or whether M is pure over Z in some sense. We give a weak answer to these questions and we discuss what other phenomena can be studied using the method of proof.
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