Epsilon constants and orthogonal representations

Darren Glass

Type: Article

Publication Date: 2004-09-01

Citations: 2

DOI: https://doi.org/10.1112/s0010437x04000491

Abstract

HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button. 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.

Locations

arXiv (Cornell University) - View - PDF
Compositio Mathematica - View - PDF

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Works Cited by This (6)

Action	Title	Year	Authors
+	Functional equations of $L$-functions of varieties over finite fields	1984	Shuji Saito
+	On the $\epsilon$ -constants of arithmetic schemes	1998	Ted Chinburg Boas Erez G. Pappas Michael Taylor
+	On the functional equation of the ArtinL-function for characters of real representations	1973	A. Fröhlich Jacques Queyrut
+	On the E-constants of a variety over a finite field	1997	Ted Chinburg Boas Erez G. Pappas M. J. Taylor
+	Local factorization of determinants of twisted DR cohomology groups	1992	Greg W. Anderson
+	ɛ-Constants and the Galois Structure of de Rham Cohomology	1997	Ted Chinburg Boas Erez G. Pappas M. J. Taylor