Cohomologie non ramifiée dans le produit avec une courbe elliptique

Abstract

A method of Gabber (2002) produces unramified cohomology classes in the products of certain varieties with an elliptic curve. The connection between third unramified cohomology and integral Hodge conjecture for codimension 2 cycles (2012, which builds upon results from algebraic K-Theory, then gives many examples of such a product for which this conjecture fails. The special case of the product with an Enriques surface was established by Benoist and Ottem (2018).

arXiv comment6 pages, in French; proof of main theorem identical to previous version; examples of applications to products with varieties other than Enriques surfaces added