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Deligne’s integrality theorem in unequal characteristic and rational points over finite fields (with an Appendix by Pierre Deligne and Hélène Esnault)
If V is a smooth projective variety defined over a local field K with finite residue field, so that its étale 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 …