Torsion cohomology classes and algebraic cycles on complex projective manifolds

C. Soule (1) , C. Voisin (2)

1 IHES - Institut des Hautes Études Scientifiques
2 IMJ - Institut de Mathématiques de Jussieu

Atiyah and Hirzebruch gave examples ofeven degree torsion classes in the singularcohomology of a smooth complex projective manifold, which arenot Poincaré dual to an algebraiccycle. We notice that the order ofthese classes are small comparedto the dimension of the manifold. However, building upon a construction of Kollàr, one can provide such examples witharbitrary high prime order, the dimension being fixed. This method alsoprovides examples of torsion algebraiccycles, which are non trivial in the Griffiths' groups, and lie in a arbitrary high level of the H.Saito filtration on Chow groups.

Mots clés: Torsion cohomology classes; algebraic cycles; complex manifolds; K-theory; cobordism

Domaines: Géométrie algébrique [math.AG]

C. Soule, C. Voisin. Torsion cohomology classes and algebraic cycles on complex projective manifolds. 2005. ⟨hal-00001298v2⟩