Abstract
Let X be a regular scheme projective and flat over Spec(Z), equidimensional of relative dimension d. Consider the Hasse-Weil zeta function of X, ζ(X, s) = ∏ x(1 −N(x) −s)−1 where x ranges over the closed points of X and N(x) is the order of the residue field of x. Denote by L(X, s) the zeta function with Γ-factors L(X, s) = ζ(X, s)Γ(X, s). The L-function conjecturally satisfies a functional equation
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