# Pfaffians, the G-Signature Theorem and Galois Hodge Discriminants

Chinburg, Ted and Pappas, Georgios and Taylor, Martin J. (2007) Pfaffians, the G-Signature Theorem and Galois Hodge Discriminants. Compositio Mathematica, 143 (5). pp. 1213-1254. ISSN 0010-437X

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 $\varepsilon_0$-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 cohomology. We also use such Pfaffian invariants, along with equivariant Arakelov Euler characteristics, to determine hermitian Euler characteristics associated to tame actions of finite groups on regular projective schemes over $\mathbb{Z}$.