Decomposition of cohomology classes in finite field extensions

Rost and Voevodsky proved the Bloch-Kato conjecture relating Milnor k-theory and Galois cohomology. It implies that if a field F contains a primitive pth root of unity, then the Galois cohomology ring of F with coefficients in the trivial F-module with p elements is generated by elements of degree one. In this talk, I will discuss a systematic approach to studying this phenomenon in finite field extensions via decomposition fields.

This is joint work with Sunil Chebolu, Jan Minac, Cihan Okay, and Andrew Schultz.