Let η : C f,N → P 1 be a cyclic cover of P 1 of degree N which is totally and tamely ramified for all the ramification points. We determine the group of fixed points of the cyclic group µ N ∼ = Z/N Z acting on the Jacobian J N := Jac(C f,N ). For each prime ℓ distinct from the characteristic of the base field, the Tate module T ℓ J N is shown to be a free module over the ringWe also calculate the degree of the induced polarization on the new part J new N of the Jacobian.is a primitive (N/D)-th root of unity, so if ω(N/D) > 1, then (ζ N ) D − 1 is again a unit in O. It follows that J new N ∩ J D = {0} = J new N ∩ J new D if ω(N/D) > 1. Suppose that N = M p r = Dp t with r ≥ t > 0 and gcd(p, M ) = 1. In particular, p ∤ Char (K). Then pO is divisible by (1 − (ζ N ) D ), so J new N ∩ J D ⊆ J D [p]. It follows that J new N