## 2007.80: $\varepsilon$-constants and equivariant Arakelov-Euler characteristics

2007.80:
Ted Chinburg, Georgios Pappas and Martin J. Taylor
(2002)
*$\varepsilon$-constants and equivariant Arakelov-Euler characteristics.*
Annales Scientifiques De L'Ecole Normales Superieure, 35 (3).
pp. 307-352.
ISSN 0012-9593

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DOI: 10.1016/S0012-9593(02)01091-1

## Abstract

Let $\mathcal{X} \rightarrow \mathcal{Y}$ be a tame $G$-cover of regular arithmetic varieties over $\Z$ with $G$ a finite group. Assuming that $\mathcal{X}$ and $\mathcal{Y}$ have “tame” reduction we show how to determine the $\varepsilon$-constant in the conjectural functional equation of the Artin–Hasse–Weil function $L(\mathcal{X} / \mathcal{Y}, V, s)$ for $V$ a symplectic representation of $G$ from a suitably refined equivariant Arakelov–de Rham–Euler characteristic of $\mathcal{X}$. Our result may be viewed firstly as a higher dimensional version of the Cassou-Noguès–Taylor characterization of tame symplectic Artin root numbers in term of rings of integers with their trace form, and secondly as a signed equivariant version of Bloch's conductor formula.

Item Type: | Article |
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Subjects: | MSC 2000 > 11 Number theory MSC 2000 > 14 Algebraic geometry |

MIMS number: | 2007.80 |

Deposited By: | Miss Louise Stait |

Deposited On: | 21 May 2007 |

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