Conjugate varieties with distinct real cohomology algebras

2007/06/25 by François Charles, Charles, François
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.0706.3674

18 pages, final version

arxiv created 2008/07/15 · arxiv updated 2009/12/01

Abstract

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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