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arXiv · 1206.4002

The Tate conjecture for K3 surfaces over finite fields

François Charles
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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>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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François Charles. 2012-07-07. The Tate conjecture for K3 surfaces over finite fields. https://doi.org/10.1007/s00222-012-0443-y

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