Arithmetic Properties of Local Systems - Lecture 2

Explore a 50-minute lecture on arithmetic properties of local systems, delivered by Hélène Esnault from Freie University Berlin, Harvard, and University of Copenhagen as part of the IAS PCMI Park City Mathematics Institute's 2024 program on Motivic Homotopy Theory. Delve into the fundamental group of varieties in topology and arithmetic geometry, examining how local systems and linear representations modulo conjugation serve as analytical tools despite information loss. Learn about the obstructions that prevent finitely presented groups from being fundamental groups of smooth complex quasi-projective varieties, with special attention to motivic obstructions. Access comprehensive lecture notes and slides while building upon prerequisites in algebraic geometry, algebraic topology, homotopy theory, and beneficial knowledge of Galois and étale cohomology. Participate in daily problem sessions designed to reinforce understanding of this advanced mathematical content within a collaborative environment featuring researchers at various career stages.