Overview
Explore a comprehensive lecture on G-torsors and G-bundles in algebraic geometry through this one-hour presentation from the IAS PCMI Park City Mathematics Institute. Delve into the theory of torsors over Dedekind rings, including the ring of integers Z and affine curves over arbitrary fields. Examine key cases like the affine line (Raghunathan-Ramanathan, 1984) and punctured affine line while learning about étale cohomology and patching techniques. Access supplementary materials including detailed lecture notes and problem sets to reinforce understanding of topics like three-point Lie algebras, quadratic bundles, and the Grothendieck-Serre conjecture over semilocal Dedekind rings. Part of the 2024 Program on Motivic Homotopy Theory, this advanced mathematical discussion requires foundational knowledge in algebraic geometry, algebraic topology, homotopy theory, and familiarity with Galois and étale cohomology.
Syllabus
Torsors over affine curves part2 | Philippe Gille, Université Claude Bernard, Lyon 1
Taught by
IAS | PCMI Park City Mathematics Institute