Conjugate varieties with distinct real cohomology algebras

Details Conjugate varieties with distinct real cohomology algebras Conjugate varieties with distinct real cohomology algebras

2007-06-25

arxiv.org/abs/0706.3674v3

Mathematics

Algebraic Geometry

18 pages, final version

Scientific paper

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.

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