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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)
2006
Annals of Mathematics
Preserved Fulltext
If V is a smooth projective variety defined over a local field K with finite residue field, so that itsétale cohomology over the algebraic closureK 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.
doi:10.4007/annals.2006.164.715
fatcat:pjyk2cvlbrbsrkhb42msbsrj2i