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Let   $p$   be an odd prime and let   $k$   be a field finitely generated over the finite field with   $p$   elements. For any K3 surface   $X$   over   $k,$   we prove that the cokernel of the natural map   $\textrm {Br}(k)\to \textrm {Br}(X)$   is finite modulo the   $p$  -primary torsion subgroup.

A Finiteness Theorem for the Brauer Group of K3 Surfaces in Odd Characteristic