# Milnor conjecture

In mathematics, the Milnor conjecture was a proposal by John Milnor (1970) of a description of the Milnor K-theory (mod 2) of a general field F with characteristic different from 2, by means of the Galois (or equivalently étale) cohomology of F with coefficients in Z/2Z. It was proved by Vladimir Voevodsky (1996, 2003a, 2003b).

## Statement of the theorem

Let F be a field of characteristic different from 2. Then there is an isomorphism

${\displaystyle K_{n}^{M}(F)/2\cong H_{{\acute {e}}t}^{n}(F,\mathbb {Z} /2\mathbb {Z} )}$

for all n ≥ 0, where KM denotes the Milnor ring.