Alas, Grothendieck was unable to prove the Standard Conjectures.


They remain unproved to this day!


It's still not known if \(\mathsf{Mot}\) has the desirable properties I just listed.


Deligne proved the Riemann Hypothesis for varieties over finite fields in 1974 in a way that sidestepped these questions.


Thus, motives remain deeply mysterious.

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