most recent 30 from http://mathoverflow.net 2013-06-20T00:47:40Z http://mathoverflow.net/feeds/question/46415 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/46415/a-hodge-substructure-with-nice-weight-factors-that-does-not-correspond-to-a-mi Mikhail Bondarko 2010-11-17T21:57:19Z 2010-11-17T22:07:31Z

<p>Suppose that we have a mixed motif $M$ with only two (subsequent) weights, and have a subobject for each weight factor. How we can control whether there exists a submotif of $M$ with these two factors? It seems that here the existence of a mixed Hodge substructure with the corresponding weight factors in the singular cohomology of $M$ is not sufficient, since the corresponding mixed motivic $Ext^1$ does not inject into its Hodge 'realization'. Is this correct? What happens here if the base field is a number field? Are there any examples here that are well understood (certainly, the matter is very conjectural)? </p>