Arithmetic and the representation theory of fundamental groups

Daniel Litt
Institute for Advanced Study

We discuss geometric (and function field) analogues of several well-known theorems and conjectures in number theory, including Mazur's torsion theorem, the Fontaine-Mazur finiteness conjecture, and the Frey-Mazur conjecture. We use anabelian techniques to prove these function field analogues, including some results which are new for Riemann surfaces.

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