no. 2
Algebraic Geometry
Coniveau over p-adic fields and points over finite fields
[Coniveau sur un corps p-adique et points sur un corps fini]
Présenté par : Pierre Deligne
Esnault, Hélène1
1 Universität Duisburg-Essen, Mathematik, 45117 Essen, Germany
Comptes Rendus. Mathématique, Tome 345 (2007) no. 2, pp. 73-76

If the ℓ-adic cohomology of a projective smooth variety, defined over a p-adic field K with finite residue field k, is supported in codimension ⩾1, then any model over the ring of integers of K has a k-rational point.

Si la cohomologie ℓ-adique d'une variété projective, lisse, définie sur un corps p-adique K à corps residuel fini k, est supportée en codimension ⩾1, alors tout modèle sur l'anneau des entiers de K a un point rationnel.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.05.017

Esnault, Hélène 1

1 Universität Duisburg-Essen, Mathematik, 45117 Essen, Germany 
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Esnault, Hélène. Coniveau over $ \mathfrak{p}$-adic fields and points over finite fields. Comptes Rendus. Mathématique, Tome 345 (2007) no. 2, pp. 73-76. doi: 10.1016/j.crma.2007.05.017

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[2] Deligne, P. La conjecture de Weil, II, Publ. Math. IHES, Volume 52 (1981), pp. 137-252

[3] Esnault, H. Deligne's integrality theorem in unequal characteristic and rational points over finite fields, with an appendix with P. Deligne, Ann. Math., Volume 164 (2006), pp. 715-730

[4] Fujiwara, K. A proof of the absolute purity conjecture (after Gabber), Azumino (Advanced Studies in Pure Mathematics), Volume vol. 36, Mathematical Society of Japan (2002), pp. 153-183

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