Field Arithmetic and the Complexity of Galois Cohomology - Part 3

Explore advanced mathematical concepts in this lecture from the Graduate Summer School at PCMI, where Daniel Krashen from the University of Pennsylvania delves into field arithmetic and Galois cohomology. Learn about fundamental questions in Galois cohomology, including their natural emergence as invariants of algebraic objects and their role as obstructions in algebraic and arithmetic geometry. Examine topics such as cohomological invariants, the structure of Galois cohomology rings, period-index problems, symbol length, and the relationship between Diophantine and cohomological dimensions. Gain insights into various techniques including Milnor conjectures, quadratic forms, and local-global principles. Access accompanying lecture notes and problem sets to reinforce understanding of these advanced mathematical concepts. Part of the 2024 Program on Motivic Homotopy Theory, this lecture requires foundational knowledge in algebraic geometry, algebraic topology, homotopy theory, and familiarity with Galois and étale cohomology.