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Deligne's integrality theorem in unequal characteristic and rational points over finite fields; and Appendix (w/Pierre Deligne)

Hélène Esnault
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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 $\bar{K}$ 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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Hélène Esnault. 2007-02-16. Deligne's integrality theorem in unequal characteristic and rational points over finite fields; and Appendix (w/Pierre Deligne). https://arxiv.org/abs/math/0405318

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