# Questions on standard (motivic) conjectures

1. Over an (algebraically closed) characteristic $p$ field, is it known that the cohomological equivalence of cycles relation (with respect to $\mathbb{Q}_l$-adic \'etale cohomology) does not depend on the choice of a prime $l$ (distinct from $p$). At least, is it known that: if the numerical equivalence of cycles relation coincides with the cohomological one for one value of $l$, this is also true for all other $l$'s?

2. I believe that in order to have Kunneth decompositions for cohomological (pure) motives and the Standard Lefshetz conjecture is suffices for the numerical equivalence of cycles relation to coincide with the cohomological one. Is this true, or does the Hodge Standard conjecture play some role here (or in the first question)?

-