Abstract

Using a theorem of Gabber on alterations, we prove a result describing the prime-to-p torsion part of the unramified Brauer group of a smooth and geometrically integral variety V over a global field of characteristic p by evaluating the elements of Br V at its local points. (C) 2013 Academie des sciences. Publie par Elsevier Masson SAS. Tous droits reserves.