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If it's a counterexample to BSD, that would be pretty surprising.

It would also be a considerably more impressive achievement, because experts had mostly shifted to Navier-Stokes regularity being false, while as far as I know almost everybody thinks BSD is true. Hodge people seem less sure about.

If either conjecture is true and they prove it, that would be an even bigger success, since the techniques might unlock any number of other theorems.

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