ε-constants and equivariant Arakelov-Euler characteristics

Let X → Y be a tame G-cover of regular arithmetic varieties over Z with G a finite group. Assuming that X and Y have "tame" reduction we show how to determine the ε-constant in the conjectural functional equation of the Artin-Hasse-Weil function L(X/Y,V,s) for V a symplectic representation of G from a suitably refined equivariant Arakelov-de Rham-Euler characteristic of X. Our result may be viewed firstly as a higher dimensional version of the Cassou-Noguès-Taylor characterization of tame symplectic Artin root numbers in term of rings of integers with their trace form, and secondly as a signed equivariant version of Bloch's conductor formula. © 2002 Éditions scientifiques et médicales Elsevier SAS.