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Feb 25, 2018 at 14:51 comment added Denis Nardin The Quillen-Lichtenbaum conjecture is a consequence of the Bloch-Kato conjecture plus the motivic spectral sequence. That is to say, there is a spectral sequence converging to the fiber of $K\to K^{ét}$ whose $E_2$-page is the difference between étale and motivic cohomology. Measuring said difference is probably going to be very hard.
Feb 25, 2018 at 14:23 history asked John Berman CC BY-SA 3.0