Coniveau over $ \mathfrak{p}$-adic fields and points over finite fields

Hélène Esnault

doi:10.1016/j.crma.2007.05.017

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

Hélène Esnault ¹

¹ Universität Duisburg-Essen, Mathematik, 45117 Essen, Germany

Comptes Rendus. Mathématique, Volume 345 (2007) no. 2, pp. 73-76.

Résumé
Abstract

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.

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.

Reçu le : 2007-04-26
Accepté le : 2007-05-06
Publié le : 2007-07-05

DOI : 10.1016/j.crma.2007.05.017

Affiliations des auteurs :

Hélène Esnault ¹

¹ Universität Duisburg-Essen, Mathematik, 45117 Essen, Germany

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     title = {Coniveau over $ \mathfrak{p}$-adic fields and points over finite fields},
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     doi = {10.1016/j.crma.2007.05.017},
     language = {en},
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Hélène Esnault. Coniveau over $ \mathfrak{p}$-adic fields and points over finite fields. Comptes Rendus. Mathématique, Volume 345 (2007) no. 2, pp. 73-76. doi : 10.1016/j.crma.2007.05.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.05.017/

Bibliographie
Cité par

[1] A.J. de Jong Families of curves and alterations, Ann. Inst. Fourier, Volume 47 (1997) no. 2, pp. 599-621

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

[3] H. Esnault 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] K. Fujiwara 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

Jason Starr; Chenyang Xu Rational points of rationally simply connected varieties over global function fields, Annales Henri Lebesgue, Volume 3 (2020), pp. 1399-1417 | DOI:10.5802/ahl.65 | Zbl:1481.14044
Jean-Louis Colliot-Thélène Variétés presque rationnelles, leurs points rationnels et leurs dégénérescences, Arithmetic Geometry, Volume 2009 (2011), p. 1 | DOI:10.1007/978-3-642-15945-9_1
Ryushiro SAKAMOTO; Heiji YASUI; Shigehiko SAKAMOTO Development of Wheel Surface Forming Technique for Ultra-smoothness Vertical Surface Grinding Method (2nd Report), Journal of the Japan Society for Precision Engineering, Volume 75 (2009) no. 12, p. 1423 | DOI:10.2493/jjspe.75.1423
Heiji YASUI; Ryushiro SAKAMOTO Development of Wheel Surface Forming Technique for Ultra-smoothness Vertical Surface Grinding Method (1st Report), Journal of the Japan Society for Precision Engineering, Volume 75 (2009) no. 5, p. 634 | DOI:10.2493/jjspe.75.634
Hélène Esnault; Chenyang Xu Congruence for rational points over finite fields and coniveau over local fields, Transactions of the American Mathematical Society, Volume 361 (2009) no. 5, pp. 2679-2688 | DOI:10.1090/s0002-9947-08-04629-1 | Zbl:1168.14017
Yuki YAMAMOTO; Heiji YASUI; Ryushiro SAKAMOTO; Yusuke TANAKA Development of Polishingless Ultra-Smoothness Grinding Method (2nd Report), Journal of the Japan Society for Precision Engineering, Volume 74 (2008) no. 9, p. 944 | DOI:10.2493/jjspe.74.944

Cité par 6 documents. Sources : Crossref, zbMATH

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