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We show that the dual of the Witt vectors on Z_{\geq 0}^n - 0 as defined byAngeltveit, Gerhardt, Hill, and Lindenstrauss represent the functor taking acommutative formal group G to the maps of formal schemes Ahat^n -> G, and thatthe Witt vectors are self-dual for Q-algebras or when n=1.

Cartier's first theorem for Witt vectors on Z_{>= 0}^n - 0