Local Systems in Arithmetic Geometry

Explore fundamental group theory in arithmetic geometry through this lecture that examines local systems as linear representations modulo conjugation. Delve into the building blocks of homotopy theory while investigating the limitations and insights gained from studying fundamental groups of varieties in both topology and arithmetic geometry. Learn about motivic obstructions that arise when determining whether a finitely presented group can serve as the fundamental group of a smooth complex quasi-projective variety. Part of the 2024 Graduate Summer School Program on Motivic Homotopy Theory, this advanced mathematical discussion requires background knowledge in algebraic geometry, algebraic topology, and homotopy theory, with additional understanding of Galois cohomology and étale cohomology being beneficial. Access comprehensive lecture notes and slides to supplement the 54-minute presentation delivered by Hélène Esnault from FU Berlin, Harvard, and Copenhagen.