$ε$-Constants and Orthogonal Representations

Details $ε$-Constants and Orthogonal Representations $ε$-Constants and Orthogonal Representations

2002-09-18

arxiv.org/abs/math/0209228v1

Mathematics

Number Theory

20 pages

Scientific paper

In this paper we suppose G is a finite group acting tamely on a regular projective curve X over 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 $\epsilon(X/G,V)$ in terms of data associated to the archimedean place and to the crossing points of irreducible components of finite fibers of X, subject to certain standard hypotheses about these fibers.

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