Arithmetic Properties of Local Systems in Motivic Homotopy Theory

Explore a 58-minute lecture on arithmetic properties of local systems delivered by Tom Bachmann from Johannes Gutenberg University of Mainz at the IAS PCMI Park City Mathematics Institute. Delve into the fundamental group of varieties in topology and arithmetic geometry through the lens of local systems and their linear representations modulo conjugation. Learn about motivic local systems and examine deep conjectures predicting when local systems should be motivic across various fields. Discover classical and recent conjectures, problems, and results in arithmetic geometry, referencing the state-of-the-art developments from Spring 2023 documented in Springer Lecture Notes 2337. Part of the 2024 Program on Motivic Homotopy Theory, this lecture requires foundational knowledge in algebraic geometry, algebraic topology, and homotopy theory, with additional background in Galois cohomology and étale cohomology being beneficial. Please note that there is an audio interruption at the 16:30 mark.