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(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

February 08, 2019 (02:00 PM PST - 03:00 PM PST)
Speaker(s): Akshay Venkatesh (Institute for Advanced Study)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC



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.

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