Epsilon constants and equivariant Arakelov Euler characteristics

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

2000-06-13

arxiv.org/abs/math/0006095v1

Mathematics

Number Theory

54 pages, LaTex

Scientific paper

We study equivariant Arakelov-Euler characteristics of hermitian sheaves on arithmetic varieties which support a tame action by a finite group G. The tameness of the group action allows us to produce an equivariant Arakelov-Euler characteristic in a particularly fine "projective" arithmetic class group. We then show that the equivariant Arakelov-Euler characteristics of various complexes of differentials determine the epsilon constants of the L-functions of the motives obtained from the arithmetic variety using symplectic representations of the group G. Our results may be viewed firstly as a higher dimensional version of the Cassou-Nogu\`{e}s Taylor characterization of symplectic Artin root numbers in terms of the hermitian structure of rings of integers, and secondly as a signed equivariant version of Bloch's conductor formula.

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