%0 Generic %1 charles2012conjecture %A Charles, François %D 2012 %K conjecture finite k3 surfaces tate %T The Tate conjecture for K3 surfaces over finite fields %U http://arxiv.org/abs/1206.4002 %X 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.

@misc{charles2012conjecture, 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.}, added-at = {2013-12-23T06:36:58.000+0100}, author = {Charles, François}, biburl = {https://www.bibsonomy.org/bibtex/2882529989d80fa8373fc01bf04d79333/aeu_research}, description = {The Tate conjecture for K3 surfaces over finite fields}, interhash = {b260dfc709445a0611091faa193e16f4}, intrahash = {882529989d80fa8373fc01bf04d79333}, keywords = {conjecture finite k3 surfaces tate}, note = {cite arxiv:1206.4002Comment: 20 pages, minor changes. Theorem 4 is stated in greater generality, but proofs don't change. Comments still welcome}, timestamp = {2013-12-23T06:36:58.000+0100}, title = {The Tate conjecture for K3 surfaces over finite fields}, url = {http://arxiv.org/abs/1206.4002}, year = 2012 }