Zero-cycles on varieties over $p$-adic fields and Brauer groups

Saito, Shuji; Sato, Kanetomo

doi:10.24033/asens.2220

Zero-cycles on varieties over

p

-adic fields and Brauer groups
[Zéro-cycles sur les variétés sur des corps

p

-adiques et groupes de Brauer]

Saito, Shuji ; Sato, Kanetomo

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 47 (2014) no. 3, pp. 505-537.

Résumé
Abstract

Dans cet article, nous étudions l'accouplement de Brauer-Manin des variétés propres et lisses sur un corps $p$ -adique, et déterminons la partie $p$ -adique de l'image de l'application cycle induite. Nous calculons aussi le $A_{0}$ d'une surface potentiellement rationnelle déployée sur une extension sauvagement ramifiée.

In this paper, we study the Brauer-Manin pairing of smooth proper varieties over a $p$ -adic field, and determine the $p$ -adic part of the image of the induced cycle map. We also compute $A_{0}$ of a potentially rational surface which splits over a wildly ramified extension.

Publié le : 2014-09-24

MR Zbl | 1 citation dans Numdam

DOI : 10.24033/asens.2220

Classification : 14C25, 14F22, 11G25.
Keywords: Brauer-Manin pairing, Chow group of zero-cycles, cycle map.
Mot clés : Accouplement de Brauer-Manin, groupe de Chow des zéro-cycles, application cycle.

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     author = {Saito, Shuji and Sato, Kanetomo},
     title = {Zero-cycles on varieties over $p$-adic fields and {Brauer} groups},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {505--537},
     publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es},
     volume = {Ser. 4, 47},
     number = {3},
     year = {2014},
     doi = {10.24033/asens.2220},
     mrnumber = {3239097},
     zbl = {1329.14057},
     language = {en},
     url = {http://www.numdam.org/articles/10.24033/asens.2220/}
}

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Saito, Shuji; Sato, Kanetomo. Zero-cycles on varieties over $p$-adic fields and Brauer groups. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 47 (2014) no. 3, pp. 505-537. doi : 10.24033/asens.2220. http://www.numdam.org/articles/10.24033/asens.2220/

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