Torsors Over Affine Curves - Part 4

Explore a 57-minute lecture from the IAS Park City Mathematics Institute's series on G-torsors and G-bundles in algebraic geometry, focusing on their behavior over affine curves and Dedekind rings. Delve into the triviality of G-torsors for semisimple k-groups over algebraically closed fields, examine special cases like the affine line and punctured affine line using étale cohomology and patching techniques, and investigate applications to affine smooth surfaces. Learn from comprehensive lecture notes and problem sets while building on prerequisites in algebraic geometry, topology, and cohomology theory. Part of the 2024 Graduate Summer School program on Motivic Homotopy Theory, this advanced mathematical exploration connects to broader themes in arithmetic geometry and algebraic topology.