Multiplicity and concentration results for fractional Schr\"odinger-Poisson equations with magnetic fields and critical growth

We deal with the following fractional Schr"odinger-Poisson equation with magnetic field \begin{equation} \varepsilon^{2s}(-\Delta){A/\varepsilon}^{s}u+V(x)u+\varepsilon^{-2t}(|x|^{2t-3}|u|^{2})u=f(|u|^{2})u+|u|^{2^{}{s}-2}u \quad \mbox{in} $\mathbb{R}$^{3}, \nonumber \end{equation} where $\epsilon >0$ is a small parameter, $s\in (\frac{3}{4},1)$, $t\in (0,1)$, $2_s^{\ast }=\frac{6}{3-2s}$ is the fractional critical exponent, $(-\mathrm{\Delta }{)}_A^s$ is the fractional magnetic Laplacian, $V:{\mathbb{R}}^3\to \mathbb{R}$ is a positive continuous potential, $A:{\mathbb{R}}^3\to {\mathbb{R}}^3$ is a smooth magnetic potential and $f:\mathbb{R}\to \mathbb{R}$ is a subcritical nonlinearity. Under a local condition on the potential $V$, we study multiplicity and concentration of nontrivial solutions as $\epsilon \to 0$. In particular, we relate the number of nontrivial solutions with the topology of the set where the potential $V$ attains its minimum.