ABSTRACT
More generally, we shall be interested in the number of solutions of the equations fα(x) = 0 in a finite field of order pe, for e = 1, 2, ... ; this number will be denoted 2 by Nf (pe).
1.2. Definition of NX(p) : the scheme setting Consider a scheme X of finite type over Z ; this assumption means that X has a finite covering by open subschemes of the form SpecA with A of finite type over Z. [In the affine case above, one has X = SpecA, where A = Z[X]/(fα).]
We denote by X/Q the generic fiber of X → SpecZ, i.e. the Q-algebraic variety deduced from X by the base change Z→ Q.
