Supersingular Tate conjecture for irreducible symplectic varieties of known types: I

We prove that for a supersingular irreducible symplectic variety admitting suitable lifting to characteristic zero has Tate Chow motive if it is of deformation type $K{3}^{[n]}$, OG6 (with Artin invariant $\mathrm{\ne }$ 4), or OG10 (with Artin invariant $\mathrm{\ne }$ 12), and has supersingular abelian Chow motive if it is of ${\mathrm{K}\mathrm{u}\mathrm{m}}^n$-type (with Artin invariant $\mathrm{\ne }$ 3). In particular, any product of those irreducible symplectic varieties satisfies the supersingular Tate conjecture for the whole $\mathrm{\ell }$-adic or crystalline cohomology ring.