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Nov 5, 2013 at 11:18 comment added jmc 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.
Jan 4, 2013 at 18:38 comment added Donu Arapura 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.
Jan 4, 2013 at 12:03 history asked IMeasy CC BY-SA 3.0