On the integral Hodge conjecture for real varieties, II

Olivier Benoist (1, 2) , Olivier Wittenberg (1, 3)

1 CNRS - Centre National de la Recherche Scientifique
2 IRMA - Institut de Recherche Mathématique Avancée
3 DMA - Département de Mathématiques et Applications - ENS Paris

We establish the real integral Hodge conjecture for 1-cycles on various classes of uniruled threefolds (conic bundles, Fano threefolds with no real point, some del Pezzo fibrations) and on conic bundles over higher-dimensional bases which themselves satisfy the real integral Hodge conjecture for 1-cycles. In addition, we show that rationally connected threefolds over non-archimedean real closed fields do not satisfy the real integral Hodge conjecture in general and that over such fields, Bröcker's EPT theorem remains true for simply connected surfaces of geometric genus zero but fails for some K3 surfaces.

Domaines: Mathématiques [math]; Géométrie algébrique [math.AG]

Olivier Benoist, Olivier Wittenberg. On the integral Hodge conjecture for real varieties, II. Journal de l'École polytechnique — Mathématiques, 2020, 7, pp.373-429. ⟨10.5802/jep.120⟩. ⟨hal-02358006⟩