  Let X be a regular scheme, projective and flat over Spec \mathbb Z. We give a
conjectural formula, up to sign and powers of 2, for \zeta^*(X,r), the leading
term in the series expansion of \zeta(X,s) at s=r, in terms of Weil-etale
motivic cohomology, singular cohomology, and derived de Rham cohomology. This
formula builds on work of Fontaine and Perrin-Riou replacing \mathbb
Q_structuers by \mathbb Z-structures.
  We show that our conjectured formula is compatible with Serre's functional
equation for the zeta function of X.
