[Wikipedia](http://en.wikipedia.org/wiki/Special_values_of_L-functions) says:



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> this circle of ideas is distinct from the Bloch–Kato conjecture of K-theory, extending the Milnor conjecture, a proof of which was announced in 2009
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What exactly is the K-theory conjecture of Bloch-Kato and has it been proven?



Proof of Bloch-Kato conjecture of K-theory?
[Here](http://www.math.rutgers.edu/~weibel/papers-dir/Bloch-Kato.pdf) are some lectures by Charles Weibel. Early on, they discuss Milnor Conjecture and Bloch-Kato, and they should go through the proof. My understanding is that there were a bunch of people involved in the proof, though a few were a bit reticent to actually write up their parts of it, and so Weibel drew the short straw and is the one writing it up.


EDIT: Adding a bit, [here's](http://www.math.rutgers.edu/~weibel/motivic2006.html) Weibel's 2006 page where he notes the status as of then, and to make sure that this is roughly self-contained, here's the statement:



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> For an odd prime $\ell$, and a field $k$ containing $1/\ell$, the Milnor K-theory $K^M\_n(k)/\ell$ is isomorphic to the étale cohomology $H^n\_{ét}(k,μ\_\ell^n)$
>  of the field $k$ with coefficients in the twists of $μ\_\ell$. 
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