Brauer Groups on K3 Surfaces and Arithmetic Applications

  title={Brauer Groups on K3 Surfaces and Arithmetic Applications},
  author={Kelly L. McKinnie and Justin Sawon and Sho Tanimoto and Anthony V{\'a}rilly-Alvarado},
  journal={arXiv: Algebraic Geometry},
For a prime p, we study subgroups of order p of the Brauer group Br(S) of a general complex polarized K3 surface of degree 2d, generalizing earlier work of van Geemen. These groups correspond to sublattices of index p of the transcendental lattice T S of S; we classify these lattices up to isomorphism using Nikulin’s discriminant form technique. We then study geometric realizations of p-torsion Brauer elements as Brauer-Severi varieties in a few cases via projective duality. We use one of these… 
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