Anna Cadoret and her collaborators have recently proved the analogue of the celebrated theorem that Deligne published in 1980 [D80]. The latter was established for l-adic cohomology while the result of [CHT17] holds for étale cohomology with finite coefficients. This result gives a new enlight in the frame of étale cohomology to one of the most fascinating conjectures of algebraic geometry, the semi-simplicity conjecture.
To read more about this result: link to the article in French
[D80] P. Deligne, La conjecture de Weil : II, Publ. Math. I.H.E.S 52, 1980, p. 137—252.
[CHT17] A. Cadoret, C.Y. Hui et A. Tamagawa, Geometric monodromy - semisimplicity and maximality, to appear in Annals of Math. 186 (juillet 2017), link on arXiv.