Deligne’s integrality theorem in unequal characteristic and rational points over finite fields (with an Appendix by Pierre Deligne and Hélène Esnault)
Annals of mathematics, Tome 164 (2006) no. 2, pp. 715-730
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.
@article{10_4007_annals_2006_164_715,
author = {H\'el\`ene Esnault },
title = {Deligne{\textquoteright}s integrality theorem in unequal characteristic and rational points over finite fields (with an {Appendix} by {Pierre} {Deligne} and {H\'el\`ene} {Esnault)}},
journal = {Annals of mathematics},
pages = {715--730},
year = {2006},
volume = {164},
number = {2},
doi = {10.4007/annals.2006.164.715},
mrnumber = {2247971},
zbl = {1111.14011},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2006.164.715/}
}
TY - JOUR AU - Hélène Esnault TI - Deligne’s integrality theorem in unequal characteristic and rational points over finite fields (with an Appendix by Pierre Deligne and Hélène Esnault) JO - Annals of mathematics PY - 2006 SP - 715 EP - 730 VL - 164 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2006.164.715/ DO - 10.4007/annals.2006.164.715 LA - en ID - 10_4007_annals_2006_164_715 ER -
%0 Journal Article %A Hélène Esnault %T Deligne’s integrality theorem in unequal characteristic and rational points over finite fields (with an Appendix by Pierre Deligne and Hélène Esnault) %J Annals of mathematics %D 2006 %P 715-730 %V 164 %N 2 %U http://geodesic.mathdoc.fr/articles/10.4007/annals.2006.164.715/ %R 10.4007/annals.2006.164.715 %G en %F 10_4007_annals_2006_164_715
Hélène Esnault . Deligne’s integrality theorem in unequal characteristic and rational points over finite fields (with an Appendix by Pierre Deligne and Hélène Esnault). Annals of mathematics, Tome 164 (2006) no. 2, pp. 715-730. doi: 10.4007/annals.2006.164.715
Cité par Sources :