ABSTRACT
The original Sato-Tate conjecture (which recently became a theorem) was about an elliptic curve X over Q, with no complex multiplication : if the corresponding NX(p) is written as p+ 1− ap, it said that the ratio ap/p 12 is equidistributed in the interval [−2, 2] with respect to a measure which is independent of X, namely the Sato-Tate measure, cf. §8.1.5.2. This conjecture has a natural generalization to every motive ([Se 94, §13]).
