Normalized solutions of fractional choquard equation with critical nonlinearity

In this paper, we are concerned with normalized solutions of the fractional critical Choquard equation with a local perturbation and prescribed mass. For the L2-sub critical case, we study the mul-tiplicity of normalized solutions by applying the truncation technique, the concentration-compactness principle and the genus theory. For the L2-supercritical case, we obtain a couple of normalized solutions by de-veloping a fiber map and using the concentration-compactness principle.