# Milnor conjecture

(Redirected from Milnor's 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

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

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