Single-peak solutions of the critical Hartree equation with electromagnetic field

In this paper, we study the following critical Hartree equation with electromagnetic field [Formula: see text] where [Formula: see text] is the imaginary unit, [Formula: see text] is the upper critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality, [Formula: see text] [Formula: see text], [Formula: see text] and [Formula: see text] is a small parameter. The magnetic potential [Formula: see text] is a bounded real-valued vector field on [Formula: see text] and [Formula: see text] denotes an electric potential. Under some suitable assumptions on [Formula: see text] and [Formula: see text], we establish the existence of single-peak solutions by applying the finite-dimensional reduction argument within the framework of critical point theory.