Finiteness of K3 surfaces  and the Tate conjecture

Lieblich, Max; Maulik, Davesh; Snowden, Andrew

doi:10.24033/asens.2215

Finiteness of K3 surfaces and the Tate conjecture
[Finitude de surfaces K3 et la conjecture de Tate]

Lieblich, Max ; Maulik, Davesh ; Snowden, Andrew

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 47 (2014) no. 2, pp. 285-308.

Résumé
Abstract

Étant donné un corps $k$ fini de caractéristique $p \geq 5$ , nous montrons que la conjecture de Tate pour les surfaces K3 sur $\bar{k}$ est vérifiée si et seulement s'il existe un nombre fini de surfaces K3 définies sur chaque extension finie de $k$ .

Given a finite field $k$ of characteristic $p \geq 5$ , we show that the Tate conjecture holds for K3 surfaces over $\bar{k}$ if and only if there are only finitely many K3 surfaces defined over each finite extension of $k$ .

Publié le : 2014-09-24

MR Zbl

DOI : 10.24033/asens.2215

Classification : 14G15, 14J28.
Keywords: Tate conjecture, twisted sheaves, K3 surfaces, Fourier-Mukai equivalence.
Mot clés : Conjecture de Tate, faisceaux tordus, surfaces K3, équivalence de Fourier-Mukai.

@article{ASENS_2014__47_2_285_0,
     author = {Lieblich, Max and Maulik, Davesh and Snowden, Andrew},
     title = {Finiteness of {K3} surfaces  and the {Tate} conjecture},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {285--308},
     publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es},
     volume = {Ser. 4, 47},
     number = {2},
     year = {2014},
     doi = {10.24033/asens.2215},
     mrnumber = {3215924},
     zbl = {1329.14078},
     language = {en},
     url = {http://www.numdam.org/articles/10.24033/asens.2215/}
}

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Lieblich, Max; Maulik, Davesh; Snowden, Andrew. Finiteness of K3 surfaces  and the Tate conjecture. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 47 (2014) no. 2, pp. 285-308. doi : 10.24033/asens.2215. http://www.numdam.org/articles/10.24033/asens.2215/

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