17
$\begingroup$

What is the simplest example of a projective variety for which it is not known if Grothendieck's Standard Conjectures hold?

What is the simplest example of a flag manifold for which it is not known if Grothendieck's Standard Conjectures hold?

Improve this question
$\endgroup$

1 Answer 1

Reset to default
7
$\begingroup$

It seems that for flag manifolds everything is very easy.:) For other varieties much less is known. For example, recently there was an attempt to construct a counterexample to the Hodge conjecture in the Cartesian square of a K3 surface: http://adsabs.harvard.edu/abs/2006math......8265K It seems that a mistake was found later (I'm not quite sure); yet probably nobody at the moment knows how to prove the conjecture in this case.

Improve this answer
$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .