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

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

2004-05-17

arxiv.org/abs/math/0405318v7

Ann. of Math. (2) 164 (2006), no. 2, 715--730

Mathematics

Number Theory

16 pages

Scientific paper

If $V$ is a smooth projective variety defined over a local field $K$ with finite residue field, so that its \'etale 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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