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Conjugate varieties with distinct real cohomology algebras

Published/Copyright: March 31, 2009
Journal für die reine und angewandte Mathematik
From the journal Volume 2009 Issue 630

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.

Received: 2007-10-02
Revised: 2008-01-05
Published Online: 2009-03-31
Published in Print: 2009-May

© Walter de Gruyter Berlin · New York 2009

Articles in the same Issue

  1. Gröbner geometry of vertex decompositions and of flagged tableaux
  2. The Diophantine equation aX4 – bY2 = 1
  3. C*-algebras and self-similar groups
  4. Conjugate varieties with distinct real cohomology algebras
  5. Classification of hyperfinite factors up to completely bounded isomorphism of their preduals
  6. Ricci flow of almost non-negatively curved three manifolds
  7. Linear dependence in Mordell-Weil groups
https://doi.org/10.1515/CRELLE.2009.036

Articles in the same Issue

  1. Gröbner geometry of vertex decompositions and of flagged tableaux
  2. The Diophantine equation aX4 – bY2 = 1
  3. C*-algebras and self-similar groups
  4. Conjugate varieties with distinct real cohomology algebras
  5. Classification of hyperfinite factors up to completely bounded isomorphism of their preduals
  6. Ricci flow of almost non-negatively curved three manifolds
  7. Linear dependence in Mordell-Weil groups
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