ABSTRACT

In this chapter, the ground field is Q ; the set of prime numbers is denoted by P . We put, as usual, ΓQ = Gal(Q/Q) ; if S is a finite subset of P , we denote by ΓS the largest quotient of ΓQ that is unramified outside S, i.e. the fundamental group of SpecZ S relative to the geometric point Z → Q. If p /∈ S, we denote by σp the corresponding Frobenius element of ΓS ; it is well defined up to conjugation ; its inverse σ−1p (the “geometric Frobenius”) will be denoted by gp.