Epsilon constants and Arakelov Euler characteristics
Number Theory
2007-05-23 v1 Algebraic Geometry
Abstract
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.
Cite
@article{arxiv.math/0006088,
title = {Epsilon constants and Arakelov Euler characteristics},
author = {T. Chinburg and G. Pappas and M. J. Taylor},
journal= {arXiv preprint arXiv:math/0006088},
year = {2007}
}
Comments
15 pages, LaTex, to appear in Mathematical Research Letters