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I just read on the ALGTOP discussion list that Morel has announced a proof of the Friedlander conjecture. Question: Are there other applications besides the Milnor conjecture $H_*(G,F_p)=H_*(BG,F_p)$ for complex algebraic groups $G$? And, for an outsider to algebraic geometry, what is the motivation to consider etale cohomology and how does it relate to ordinary cohomology, i.e. how does Friedlander imply Milnor?

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Morel explains it nicely in the video (I don't have time to type up the explanation on my phone) –  David Roberts Feb 3 '12 at 2:58

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As indicated by D. Roberts, see the video of Morel's talk at the Abel Conference in honour of Milnor held very recently!

Also, see Friedlander's own historical survey!

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