  By a heuristic argument, we relate two conjectures. One is a version of
Manin's conjecture about the distribution of rational points on a Fano variety.
We concern specific singular Fano varieties, namely quotients of projective
spaces by finite group actions, and their singularities play a key role. The
other conjecture is a generalization of Malle's conjecture about the
distribution of extensions of a number field. Main tools are several Dirichlet
series and previously obtained techniques, especially the untwisting, for the
counterpart over a local field.
