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

• 成果类型: Article
• 署名作者: Maillot, V; Roessler, D
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2004.160.727
• 发表日期: 2004
• 页码: 727-754
• 关键词: fixed-point formula; abelian-varieties; analytic-torsion; logarithmic derivatives; lefschetz type

摘要

We prove that the existence of an automorphism of finite order on a Q-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 F-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 [11, p. 205](1). Our proof relies on the arithmetic fixed-point formula (equivariant arithmetic Riemann-Roch theorem) proved by K. Kohler and the second author in [13] and the vanishing of the equivariant analytic torsion for the de Rham. complex.