Higher dimension: the prime number theorem and the Chebotarev density theorem

As we shall see, the results of §7.2.1 can be reformulated as a kind of “prime number theorem” for a scheme T of arbitrary dimension ; one may then define a notion of density (cf. [Pi 97 App.B]) and prove a “Chebotarev density theorem” as in [Se 65], [Fa 84] and [Pi 97]. One can then transpose to the case of a T -scheme X almost everything done in the previous chapters for a Z-scheme.