The Tate conjecture for K3 surfaces over finite fields |
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Authors: | François Charles |
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Institution: | 1. IRMAR–UMR 6625 du CNRS, Université de Rennes 1, Campus de Beaulieu, 35042, Rennes Cedex, France
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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≥5. This implies Tate’s conjecture for K3 surfaces over finite fields of characteristic p≥5. 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≥5. |
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