  Using constructions of Voisin, we exhibit a smooth projective variety defined
over a number field k and two complex embeddings of k, such that the two
complex manifolds induced by these embeddings have non isomorphic cohomology
algebras with real coefficients. This contrasts with the fact that the
cohomology algebras with l-adic coefficients are canonically isomorphic for any
prime number l, and answers a question of Grothendieck.
