Resumen de Deligne's integrality theorem in unequal characteristic and rational points over finite fields (with an appendix by P. Deligne and H. Esnault)

Hélène Esnault

• If V is a smooth projective variety defined over a local field K with fi- nite residue field, so that its ¿etale cohomology over the algebraic closure ¯K is supported in codimension 1, then the mod p reduction of a projective regular model carries a rational point. As a consequence, if the Chow group of 0-cycles of V over a large algebraically closed field is trivial, then the mod p reduction of a projective regular model carries a rational point.