Thank you, it is also a good opportunity to learn more French :)

Thank you very much. I don't know anything about l-adic cohomology yet, but in case of char 0 the $l$-adic cohomology coincides with normal sheaf cohomology, then we have a pure algebraic proof of Hard Lefschetz. Is it true?

Are you sure the sheaves are not isomorphic, because according to this post they are math.stackexchange.com/questions/3412415/…