The Tate conjecture for K3 surfaces over finite fields

Abstract : Artin's conjecture states that supersingular K3 surfaces over finite fields have Picard number 22. In this paper, we prove Artin's conjecture over fields of characteristic p>3. This implies Tate's conjecture for K3 surfaces over finite fields of characteristic p>3. Our results also yield the Tate conjecture for divisors on certain holomorphic symplectic varieties over finite fields, with some restrictions on the characteristic. As a consequence, we prove the Tate conjecture for cycles of codimension 2 on cubic fourfolds over finite fields of characteristic p>3.
Type de document :
Article dans une revue
Inventiones Mathematicae, Springer Verlag, 2013, 194 (1), pp.119-145. <10.1007/s00222-012-0443-y>
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https://hal.archives-ouvertes.fr/hal-00709802
Contributeur : Marie-Annick Guillemer <>
Soumis le : mardi 19 juin 2012 - 14:52:04
Dernière modification le : mercredi 12 juillet 2017 - 01:15:36

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François Charles. The Tate conjecture for K3 surfaces over finite fields. Inventiones Mathematicae, Springer Verlag, 2013, 194 (1), pp.119-145. <10.1007/s00222-012-0443-y>. <hal-00709802>

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