%0 Generic %1 pera2013conjecture %A Pera, Keerthi Madapusi %D 2013 %K conjecture k3 odd surfaces tate %T The Tate conjecture for K3 surfaces in odd characteristic %U http://arxiv.org/abs/1301.6326 %X We show that the classical Kuga-Satake construction gives rise, away from characteristic 2, to an open immersion from the moduli of primitively polarized K3 surfaces (of any fixed degree) to a certain normal integral model for a Shimura variety of orthogonal type. This allows us to attach to every polarized K3 surface in odd characteristic an abelian variety such that divisors on the surface can be identified with certain endomorphisms of the attached abelian variety. Using a result of Kisin, we can then prove the Tate conjecture for K3 surfaces over finitely generated fields of odd characteristic. We also show that the moduli stack of primitively polarized K3 surfaces of degree 2d is quasi-projective and, when d is not divisible by p^2, is geometrically irreducible in characteristic p. We indicate how the same method applies to prove the Tate conjecture for co-dimension 2 cycles on cubic fourfolds.

@misc{pera2013conjecture, abstract = {We show that the classical Kuga-Satake construction gives rise, away from characteristic 2, to an open immersion from the moduli of primitively polarized K3 surfaces (of any fixed degree) to a certain normal integral model for a Shimura variety of orthogonal type. This allows us to attach to every polarized K3 surface in odd characteristic an abelian variety such that divisors on the surface can be identified with certain endomorphisms of the attached abelian variety. Using a result of Kisin, we can then prove the Tate conjecture for K3 surfaces over finitely generated fields of odd characteristic. We also show that the moduli stack of primitively polarized K3 surfaces of degree 2d is quasi-projective and, when d is not divisible by p^2, is geometrically irreducible in characteristic p. We indicate how the same method applies to prove the Tate conjecture for co-dimension 2 cycles on cubic fourfolds.}, added-at = {2013-12-23T06:34:58.000+0100}, author = {Pera, Keerthi Madapusi}, biburl = {https://www.bibsonomy.org/bibtex/21a5f0f5d878990f1b4d5dbb3130e4536/aeu_research}, description = {The Tate conjecture for K3 surfaces in odd characteristic}, interhash = {5f2f60c441806e0e59e2f96ed4bab015}, intrahash = {1a5f0f5d878990f1b4d5dbb3130e4536}, keywords = {conjecture k3 odd surfaces tate}, note = {cite arxiv:1301.6326Comment: Introduction revamped}, timestamp = {2013-12-23T06:34:58.000+0100}, title = {The Tate conjecture for K3 surfaces in odd characteristic}, url = {http://arxiv.org/abs/1301.6326}, year = 2013 }