It would be worth if we have a current state of the conjectures of
Propriétés conjecturales des groupes de Galois motiviques et des représentations l-adiques. J P Serre. In Motives, Seattle
And most important, which ones have been proved..?
Here is an example of work dedicated to the solution of one of these conjectures.
Has there been any proof of some of them since then?