# chow kunneth motivic decomposition for dummies

Hi everybody,

I have just realized that, if I had to explain Chow-Kunneth decomposition for Chow motives to someone who is a newbie of the subject, I would hardly find a way which is far from the standard definition and maybe not that easy to grasp for a beginner. What is your low-road way for explaining that? maybe some nice geometric intutition I don't have...

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It seems a bit cruel to do that to a true beginner.... but if I had to , I guess I would work out the example of curves, which isn't too bad. –  Donu Arapura Jan 4 '13 at 18:38
May we assume that your beginner knows what a variety is, and what singular cohomology is? Nevertheless, it is pretty hard to explain something to a beginner, if even experts don't know the existence. If you just want to explain what we are looking for: a direct sum decomposition: $M = \oplus M^{i}$ corresponding to the decomposition on realisations $\mathrm{H} = \oplus \mathrm{H}^{i}$. As Dona Arapura said, you can do the example for curves. Then you have also done almost all known cases... (abelian varieties, surfaces, ...) but not much more. –  jmc Nov 5 '13 at 11:18