$ε$-Constants and Orthogonal Representations

Abstract

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 $ε$-constant $ε(X/G,V)$ 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.

20 pages