In "F-isocrystals on open varieties results and conjectures" Faltings says:



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> "Finally, we extend the theory of weights and show as much as possible of the crystalline analogue of the Weil conjectures."
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> 
> 


**My questions are:** 


What is the current state of the crystalline analogue of the Weil conjectures?


Which are the articles and books about these conjectures?



What is the current state of the crystalline analogue of the Weil conjectures?
As far as I can tell, [Kedlaya solved it 12 years ago.](http://arxiv.org/abs/math/0210149) 


