Abstract: Milnor conjectured in 1970 that each etale cohomology group of a field (mod 2 coefficients) should have a presentation with units as generators and simple quadratic relations (the ring with this presentation is now called the "Milnor K-theory" of the field). This was proven by Voevodsky, but the odd version (mod p coefficients for other primes) has been open until very recently, and had been known as the Bloch-Kato Conjecture.

Using certain norm varieties, constructed by Rost, and techniques from motivic cohomology, we now know that this conjecture is true. This talk will be a non-technical overview of the ingredients that go into the proof, and why this conjecture matters to non-specialists