In this [MO answer](https://mathoverflow.net/questions/83421/voevodskys-counterexample-to-the-existence-of-a-motivic-t-structure?rq=1) of M. Bondarko, he says: 

>"the Hodge conjecture implies all the Grothendieck's standard conjectures over base fields of characteristic 0..."

and in [Remarks on Grothendieck's standard conjectures](http://arxiv.org/pdf/1006.1116v2.pdf) A. Beilinson says: 

>"We show that Grothendieck’s standard conjectures (over a field of characteristic zero) follow from either of two other motivic conjectures, namely, that of existence of the motivic t-structure and (a weak version of) Suslin’s Lawson homology conjecture".

**My question is:** What about with standard conjectures in positive characteristic?