  In present paper, we study the fractional Choquard equation
$$\varepsilon^{2s}(-\Delta)^s u+V(x)u=\varepsilon^{\mu-N}(\frac{1}{|x|^\mu}\ast
F(u))f(u)+|u|^{2^\ast_s-2}u$$ where $\varepsilon>0$ is a parameter,
$s\in(0,1),$ $N>2s,$ $2^*_s=\frac{2N}{N-2s}$ and $0<\mu<\min\{2s,N-2s\}$. Under
suitable assumption on $V$ and $f$, we prove this problem has a nontrivial
nonnegative ground state solution. Moreover, we relate the number of nontrivial
nonnegative solutions with the topology of the set where the potential attains
its minimum values and their's concentration behavior.

Functional Analysis;Analysis of PDEs