In this paper, we consider the following fractional Choquard–Kirchhoff equation with magnetic fields and critical exponents M([u]s,A2)(-Δ)Asu+V(x)u=[|x|-α∗|u|2α,s∗]|u|2α,s∗-2u+λf(x,u)inRN,\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} M([u]_{s,A}^{2})(-\Delta )_{A}^{s}u+V(x)u=[|x|^{-\alpha }*|u|^{2^{*}_{\alpha ,s}}]|u|^{2^{*}_{\alpha ,s}-2}u+\lambda f(x,u) \quad \text {in } {\mathbb {R}}^{N}, \end{aligned}$$\end{document}where N>2s\documentclass[12pt]{minimal}
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\begin{document}$$N>2s$$\end{document} with 0<s<1\documentclass[12pt]{minimal}
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\begin{document}$$0<s<1$$\end{document}, λ>0\documentclass[12pt]{minimal}
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\begin{document}$$\lambda >0$$\end{document}, A=(A1,A2,…,An)∈(RN,RN)\documentclass[12pt]{minimal}
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\begin{document}$$A=(A_{1},A_{2},\ldots ,A_{n})\in ({\mathbb {R}}^{N},{\mathbb {R}}^{N})$$\end{document} is a magnetic potential, 2α,s∗=(2N-α)/(N-2s)\documentclass[12pt]{minimal}
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\begin{document}$$2^{*}_{\alpha ,s}=(2N-\alpha )/(N-2s)$$\end{document} is the fractional Hardy—Littlewood—Sobolev critical exponent with 0<α<2s\documentclass[12pt]{minimal}
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\begin{document}$$0<\alpha <2s$$\end{document}, M([u]s,A2)=a+b[u]s,A2\documentclass[12pt]{minimal}
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\begin{document}$$M([u]_{s,A}^{2})=a+b[u]_{s,A}^{2}$$\end{document} with a,b>0\documentclass[12pt]{minimal}
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\begin{document}$$a,b>0$$\end{document}, u∈(RN,C)\documentclass[12pt]{minimal}
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\begin{document}$$u\in ({\mathbb {R}}^{N}, {\mathbb {C}})$$\end{document} is a complex valued function, V∈L∞(RN)\documentclass[12pt]{minimal}
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\begin{document}$$V\in L^{\infty }({\mathbb {R}}^{N})$$\end{document} and f∈(RN×R,R)\documentclass[12pt]{minimal}
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\begin{document}$$f\in ({\mathbb {R}}^{N}\times {\mathbb {R}},{\mathbb {R}})$$\end{document} are continuous functions, (-Δ)As\documentclass[12pt]{minimal}
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\begin{document}$$(-\Delta )^{s}_{A}$$\end{document} is a fractional magnetic Laplacian operator. Under some suitable assumptions, by applying the Nehari method and the concentration-compactness principle, we obtain the existence of ground state solutions.
