Special values of motives over Spec Z

L-functions of motives over Spec Z encompass both L-functions associated to smooth projective varieties over Q and zeta functions of schemes over Spec Z. In this talk I will state a conjecture about special values of such L-functions. This conjecture shares a kinship with Poincaré duality or Artin-Verdier duality. It is equivalent to the conjunction of the conjectures of Beilinson, Soulé and Tate and allows to take advantage of the fact that motives over Spec Z form a triangulated category.