Field Arithmetic and the Complexity of Galois Cohomology - Part 4

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 local-global principles, Milnor conjectures, and quadratic forms while accessing accompanying lecture notes and problem sets for hands-on practice. Designed for students with foundational knowledge in algebraic geometry, algebraic topology, homotopy theory, and preferably Galois and étale cohomology, this lecture is part of a comprehensive program on Motivic Homotopy Theory.