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1 results

  • Epsilon constants and orthogonal representations

  • Darren Glass
  • Journal:
    Compositio Mathematica / Volume 140 / Issue 5 / September 2004
    Published online by Cambridge University Press:
    04 December 2007, pp. 1135-1148
    Print publication:
    September 2004
    • Article
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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.