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[personal profile] lproven
In simple terms, the cohomology of a coherent sheaf over a finite field couldn't capture as much topology as singular cohomology, with integer coefficients.
From the Wikipedia article on Jean-Pierre Serre, after reading on Slashdot a story about Prof Chandrashekar Khare's breakththough regarding Serre's conjecture.

"How stupid of me not to have thought of that!" (as T H Huxley said upon reading The Origin of Species.)

If anyone would care to attempt to explain Serre's conjecture in even simpler terms than this ([livejournal.com profile] steer?), they are very welcome.
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Liam Proven

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