The quadratic Schrödinger system on ${\mathbb{T}}^6$

In this article, we study the global well-posedness for the quadratic Schrödinger system on ${\mathbb{T}}^6$. To achieve this, we utilize the concentration-compactness/rigitdity argument initiated by Ionescu and Pausader \cite{IPT3}. Our result is also regarded as a periodic analogue of Gao-Meng-Xu-Zheng \cite{GMXZ}.