On the periods of motives with complex multiplication and a conjecture of Gross-Deligne

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We prove that the existence of an automorphism of finite order on a (defined over a number field) variety X implies the existence of algebraic linear relations between the logarithm of certain periods of X and the logarithm of special values of the Gamma-function. This implies that a slight variation of results by Anderson, Colmez and Gross on the periods of CM abelian varieties is valid for a larger class of CM motives. In particular, we prove a weak form of the period conjecture of Gross-Deligne. Our proof relies on the arithmetic fixed point formula (equivariant arithmetic Riemann-Roch theorem) proved by K. Koehler and the second author, and the vanishing of the equivariant analytic torsion for the Dolbeault complex.
20 pages, submitted

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Number Theory, Algebraic Geometry, 11R42, 14K22, 14K20, 14C30, 14C40, 14G40

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http://salesiana.dossiersoluciones.com/handle/123456789/64947

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0209177
 http://arxiv.org/abs/math/0209177

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arXiv