Epsilon constants and Arakelov Euler characteristics

Details Epsilon constants and Arakelov Euler characteristics Epsilon constants and Arakelov Euler characteristics

2000-06-12

arxiv.org/abs/math/0006088v1

Mathematics

Number Theory

15 pages, LaTex, to appear in Mathematical Research Letters

Scientific paper

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.

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