most recent 30 from http://mathoverflow.net 2013-06-19T00:08:54Z http://mathoverflow.net/feeds/question/15363 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/15363/examples-for-which-it-is-not-known-if-grothendiecks-standard-conjectures-hold John McCarthy 2010-02-15T21:04:37Z 2010-02-16T14:22:22Z

<p>What is the simplest example of a projective variety for which it is not known if Grothendieck's Standard Conjectures hold?</p> <p>What is the simplest example of a flag manifold for which it is not known if Grothendieck's Standard Conjectures hold? </p>

http://mathoverflow.net/questions/15363/examples-for-which-it-is-not-known-if-grothendiecks-standard-conjectures-hold/15453#15453 Mikhail Bondarko 2010-02-16T14:22:22Z 2010-02-16T14:22:22Z

<p>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: <a href="http://adsabs.harvard.edu/abs/2006math......8265K" rel="nofollow">http://adsabs.harvard.edu/abs/2006math......8265K</a> 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. </p>