Dénombrabilité des classes d'équivalences dérivées de variétés algébriques.

Mathieu Anel (1) , Bertrand Toen (2)

1 Department of Mathematics [London, Ontario]
2 LEP - Laboratoire Émile Picard

Let $X \to S$ be a miniversal family of smooth and projective varieties and D be a fixed triangulated category. We show that the set of points s in S such that the derived category of the fiber X_s at s is equivalent to D is at most countable. We deduce from this that the derived equivalence classes of smooth and projective complex varieties is at most countable.

Domaines: Géométrie algébrique [math.AG]

Mathieu Anel, Bertrand Toen. Dénombrabilité des classes d'équivalences dérivées de variétés algébriques.. Journal of Algebraic Geometry, 2008, 18, pp.257-277. ⟨10.1090/S1056-3911-08-00487-6⟩. ⟨hal-00772932⟩