The orthonormal Strichartz inequality on torus

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In this paper, motivated by recent important works due to Frank-Lewin-Lieb-Seiringer FLLS and Frank-Sabin frank-sabin-1, we study the Strichartz inequality on torus with the orthonormal system input and obtain sharp estimates in certain sense. An application of the inequality shows the well-posedness to the periodic Hartree equation describing the infinitely many quantum particles with the power type interaction.