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| HAL: hal-00709802, version 1 |
| arXiv: 1206.4002 |
| Detailed view |  Export this paper |
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| The Tate conjecture for K3 surfaces over finite fields |
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| François Charles 1, 2 |
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| (2012-06-18) |
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| 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. |
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| 1: | Département de Mathématiques et Applications (DMA) |
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CNRS : UMR8553 – Ecole normale supérieure de Paris - ENS Paris |
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| 2: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| Géométrie algébrique |
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| Subject | : | Mathematics/Algebraic Geometry Mathematics/Number Theory |
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| Fulltext link: |
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| http://fr.arXiv.org/abs/1206.4002 |
| hal-00709802, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00709802 | |
| oai:hal.archives-ouvertes.fr:hal-00709802 | |
| From: Marie-Annick Guillemer | |
| Submitted on: Tuesday, 19 June 2012 14:52:04 | |
| Updated on: Tuesday, 19 June 2012 14:52:04 | |
