Local Systems in Arithmetic Geometry - Lecture 3

Explore fundamental group theory in arithmetic geometry through this 45-minute lecture that examines local systems as linear representations modulo conjugation. Delve into the complexities of homotopy theory while understanding the limitations and benefits of using local systems to study fundamental groups of varieties. Learn about geometric obstructions that prevent certain finitely presented groups from being fundamental groups of smooth complex quasi-projective varieties, with special emphasis on motivic obstructions. Access comprehensive lecture notes and slides that complement the discussion of deep conjectures predicting when local systems should be motivic across various fields. Part of the 2024 Program on Motivic Homotopy Theory, this advanced mathematical presentation requires foundational knowledge in algebraic geometry, algebraic topology, homotopy theory, and benefits from familiarity with Galois cohomology and étale cohomology.