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
Uncontrolled Keywords: Hodge cohomology; duality pairings; local constants; Pfaffians.
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 11 Number theory
MSC 2010, the AMS's Mathematics Subject Classification > 14 Algebraic geometry
Depositing User: Ms Lucy van Russelt
Date Deposited: 02 Oct 2007
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/798

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