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Epsilon constants and orthogonal representations

Published online by Cambridge University Press:  04 December 2007

Darren Glass
Darren Glass
Affiliation:
Department of Mathematics, Columbia University, 2990 Broadway, New York, NY 10027, [email protected]
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Abstract

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In this paper we suppose G is a finite group acting tamely on a regular projective curve $\mathcal{X}$ over $\mathbb{Z}$ and V is an orthogonal representation of G of dimension 0 and trivial determinant. Our main result determines the sign of the $\epsilon$-constant $\epsilon(\mathcal{X}/G,V)$ in terms of data associated to the archimedean place and to the crossing points of irreducible components of finite fibers of $\mathcal{X}$, subject to certain standard hypotheses about these fibers.

Keywords

Epsilon constantsL-functionsorthogonal representations11G35 (primary)11G4014G40 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 5 , September 2004 , pp. 1135 - 1148
Copyright
Foundation Compositio Mathematica 2004