Abstract

In early 1970?s Milnor introduced a K-theory which leads to a generalization of classical Kummer theory relating n-th root field extensions to the abelian Galois group of the corresponding extension. Milnor introduced a connection between K-theory and cohomological invariants of the Galois group and conjectured that this was an isomorphism. In 1995 Voevodsky proved the conjecture in characteristic 2 and received the Fields medal in 2002 ICM in China for this work. We will consider some of the concepts that go into this important recent development.



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