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In this paper, we study the following fractional Schr\"{o}dinger-Poissonsystem \begin{equation*} \left\{  \begin{array}{ll}  \varepsilon^{2s}(-\Delta)^su+V(x)u+\phi u=g(u) & \hbox{in $\mathbb{R}^3$,}  \varepsilon^{2t}(-\Delta)^t\phi=u^2,\,\, u>0& \hbox{in $\mathbb{R}^3$,}  \end{array} \right. \end{equation*} where $s,t\in(0,1)$, $\varepsilon>0$ is asmall parameter. Under some suitable assumptions on potential function $V(x)$and critical nonlinearity term $g(u)$, we construct a family of positivesolutions $u_{\varepsilon}\in H^s(\mathbb{R}^3)$ which concentrates around theglobal minima of $V$ as $\varepsilon\rightarrow0$.

Concentrating phenomenon for fractional nonlinear Schr\"{o}dinger-Poisson system with critical nonlinearity