Remarks on curve classes on rationally connected varieties

Abstract

We study for rationally connected varieties $X$ the group of degree 2 integral homology classes on $X$ modulo those which are algebraic. We show that the Tate conjecture for divisor classes on surfaces defined over finite fields implies that this group is trivial for any rationally connected variety.

A few typos corrected

References in corpus (3)

• Cohomologie non ramifiée et conjecture de Hodge entière
• The Tate conjecture over finite fields (AIM talk)
• Cycles de codimension 2 et H^3 non ramifié pour les variétés sur les corps finis

Cited by in corpus (2)

• On the integral Hodge conjecture for real varieties, I
• On the coniveau of rationally connected threefolds