John Milnor in 1970, gave a relation between 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 $\mathbb{Z}/2\mathbb{Z}$.

The precise statement is as follows:

Let $F$ be a field of characteristic different from 2. Then there is an isomorphism \[ K^M_n(F)/2\cong H^n_{et}(F,\mathbb{Z}/2\mathbb{Z})\; \forall n\ge 0.\label{} \] Voedovsky was awarded the Fields Medal in 2002 for proving the theorem for all $n$.

I discussed quadratic forms and worked on the base cases of the Milnor’s conjecture as part of my Master’s thesis.

The report is available here.