# Formality of algebraic varieties via l-adic cohomology?

The cohomology with say real coefficients of any smooth projective algebraic variety is formal, by

Deligne, Griffiths, Morgan, Sullivan: Real homotopy theory of Kähler manifolds, Inv. Math. 29, 245-274

In their introduction they write, that this was inspired by the following observation:

In the l-adic picture the higher massey products would go between spaces with different frobenius eigenvalues, hence had to vanish.

There is a $p$-adic proof of formality for smooth proper complex varieties in the paper "F-isocrystals and homotopy types" by Martin Olsson. –  ulrich Apr 30 '12 at 15:34