Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

As far as I understand, the category of pure polarizable Hodge modules is semi-simple, whereas the cohomology of the corresponding schemes is graded polarizable. Is it true that one doesn't have any similar results for etale cohomology since it is not known whether the corresponding bilinear forms are positive definite? Or maybe for varieties in characteristic 0 one still can prove that these form are always positive definite using the comparison of etale cohomology with singular one?

Is anything known here in the case of 'mixed' realizations (as defined by Jannsen and Huber)?

share|improve this question
1  
Your first question sounds a lot like Grothendieck's standard conjecture "Hdg", which would still be open in general. Regarding your last question, it seems that such statements are proved in Jannsen's book in chapter 1, sections 1 and 4. –  Donu Arapura Nov 5 '10 at 15:15
    
Thanks! That's exactly what I needed. –  Mikhail Bondarko Nov 6 '10 at 9:37
add comment

Know someone who can answer? Share a link to this question via email, Google+, Twitter, or Facebook.

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.