(Derived) moduli of local systems in number theory
Introductory Workshop: Derived Algebraic Geometry and Birational Geometry and Moduli Spaces January 31, 2019  February 08, 2019
Location: SLMath: Eisenbud Auditorium
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27Venkatesh
If X is a complex variety, we can form a moduli space M of local systems parameterizing representations of pi_1(X).
One would like to do the same in arithmetic situations  if X is a curve over a finite field, or the ring of integers of a number field. Here we can only construct a shadow of M, remembering some of its formal geometry. However, there are many indications that a more satisfactory theory should exist, and I will review three of them in my talk.
Notes

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27Venkatesh
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