Epsilon constants and Arakelov Euler characteristics

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We conjecture that the logarithm of the absolute value of the constant in the functional equation of the Hasse-Weil L-function of a variety X over Z is equal to a certain Arakelov de Rham Euler characteristic of X. This generalizes the fact that the constant in the functional equation of the zeta function of a number field is the square root of the discriminant of its ring of integers. We show that this conjecture is equivalent to Bloch's conjecture which expresses the conductor as the degree of a localized Chern class of the differentials. We prove both of these conjectures in the case of "tame" reduction.
15 pages, LaTex, to appear in Mathematical Research Letters

Keywords

Number Theory, Algebraic Geometry

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/59397

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0006088
 http://arxiv.org/abs/math/0006088

Collections

arXiv