Pfaffians, the G-signature theorem and Galois Hodge discriminants

Let G be a finite group acting freely on a smooth, projective scheme X over a locally compact field of characteristic 0. We show that the ε0-constants associated to symplectic representations V of G and the action of G on X may be determined from Pfaffian invariants associated to duality pairings on Hodge cohornology. We also use such Pfaffian invariants, along with equivariant Arakelov Etiler characteristics, to determine hermitian Euler characteristics associated to tame actions of finite groups on regular projective schemes over ℤ. © Foundation Compositio Mathematica 2007.