Étant donné un corps fini de caractéristique , nous montrons que la conjecture de Tate pour les surfaces K3 sur est vérifiée si et seulement s'il existe un nombre fini de surfaces K3 définies sur chaque extension finie de .
Given a finite field of characteristic , we show that the Tate conjecture holds for K3 surfaces over if and only if there are only finitely many K3 surfaces defined over each finite extension of .
DOI : 10.24033/asens.2215
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://archive.numdam.org/articles/10.24033/asens.2215/} }
TY - JOUR AU - Lieblich, Max AU - Maulik, Davesh AU - Snowden, Andrew TI - Finiteness of K3 surfaces and the Tate conjecture JO - Annales scientifiques de l'École Normale Supérieure PY - 2014 SP - 285 EP - 308 VL - 47 IS - 2 PB - Société Mathématique de France. Tous droits réservés UR - http://archive.numdam.org/articles/10.24033/asens.2215/ DO - 10.24033/asens.2215 LA - en ID - ASENS_2014__47_2_285_0 ER -
%0 Journal Article %A Lieblich, Max %A Maulik, Davesh %A Snowden, Andrew %T Finiteness of K3 surfaces and the Tate conjecture %J Annales scientifiques de l'École Normale Supérieure %D 2014 %P 285-308 %V 47 %N 2 %I Société Mathématique de France. Tous droits réservés %U http://archive.numdam.org/articles/10.24033/asens.2215/ %R 10.24033/asens.2215 %G en %F ASENS_2014__47_2_285_0
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://archive.numdam.org/articles/10.24033/asens.2215/
Supersingular K3 surfaces, Ann. Sci. École Norm. Sup., Volume 7 (1974), p. 543-567 (1975) (ISSN: 0012-9593) | DOI | Numdam | MR | Zbl
, London Mathematical Society Monographs, 13, Academic Press Inc., 1978, 413 pages (ISBN: 0-12-163260-1) | MR | Zbl
Nonfine moduli spaces of sheaves on K3 surfaces, Int. Math. Res. Not., Volume 2002 (2002), pp. 1027-1056 (ISSN: 1073-7928) | DOI | MR | Zbl
La conjecture de Weil pour les surfaces K3, Invent. Math., Volume 15 (1972), pp. 206-226 (ISSN: 0020-9910) | DOI | MR | Zbl
, Algebraic surfaces (Orsay, 1976–78) (Lecture Notes in Math.), Volume 868, Springer, 1981, pp. 58-79 | MR | Zbl
Equivalences of twisted K3 surfaces, Math. Ann., Volume 332 (2005), pp. 901-936 (ISSN: 0025-5831) | DOI | MR | Zbl
Moduli of twisted sheaves, Duke Math. J., Volume 138 (2007), pp. 23-118 (ISSN: 0012-7094) | DOI | MR | Zbl
Twisted sheaves and the period-index problem, Compos. Math., Volume 144 (2008), pp. 1-31 (ISSN: 0010-437X) | DOI | MR | Zbl
Moduli of twisted orbifold sheaves, Adv. Math., Volume 226 (2011), pp. 4145-4182 (ISSN: 0001-8708) | DOI | MR | Zbl
On the Brauer group of a surface, Invent. Math., Volume 159 (2005), pp. 673-676 (ISSN: 0020-9910) | DOI | MR | Zbl
A note on the cone conjecture for K3 surfaces in positive characteristic (preprint arXiv:1102.3377 ) | MR
Derived equivalence of K3 surfaces in positive characteristic (in preparation)
Number of points of varieties in finite fields, Amer. J. Math., Volume 76 (1954), pp. 819-827 (ISSN: 0002-9327) | DOI | MR | Zbl
Abelian varieties (2008) (available at http://www.jmilne.org/math/CourseNotes/AV.pdf )
, Vector bundles on algebraic varieties (Bombay, 1984) (Tata Inst. Fund. Res. Stud. Math.), Volume 11, Tata Inst. Fund. Res., 1987, pp. 341-413 | MR | Zbl
Tate's conjecture for K3 surfaces of finite height, Ann. of Math., Volume 122 (1985), pp. 461-507 (ISSN: 0003-486X) | DOI | MR | Zbl
, Arithmetic and geometry, Vol. II (Progr. Math.), Volume 36, Birkhäuser, 1983, pp. 361-394 | DOI | MR | Zbl
-isocrystals and de Rham cohomology. II. Convergent isocrystals, Duke Math. J., Volume 51 (1984), pp. 765-850 (ISSN: 0012-7094) | DOI | MR | Zbl
Projective models of K3 surfaces, Amer. J. Math., Volume 96 (1974), pp. 602-639 (ISSN: 0002-9327) | DOI | MR | Zbl
, Springer, 1973, 115 pages |, Current developments in algebraic geometry (Math. Sci. Res. Inst. Publ.), Volume 59, Cambridge Univ. Press, 2012, pp. 405-426 | MR | Zbl
, Moduli spaces and arithmetic geometry (Adv. Stud. Pure Math.), Volume 45, Math. Soc. Japan, 2006, pp. 1-30 | MR | Zbl
Endomorphisms of abelian varieties and points of finite order in characteristic , Mat. Zametki, Volume 21 (1977), pp. 737-744 (ISSN: 0025-567X) | MR | Zbl
Cité par Sources :