# 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

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## Abstract

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 $\mathbb{Z}$.

Item Type: Article Hodge cohomology; duality pairings; local constants; Pfaffians. MSC 2010, the AMS's Mathematics Subject Classification > 11 Number theoryMSC 2010, the AMS's Mathematics Subject Classification > 14 Algebraic geometry Ms Lucy van Russelt 02 Oct 2007 20 Oct 2017 14:12 http://eprints.maths.manchester.ac.uk/id/eprint/798

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