Abstract
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 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.

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