2002/09/14 by V. Maillot, Maillot, V., D. Roessler +1
Mathematics · #11R42 #14C30 #14C40 #14G40 #14K20 #14K22 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11R42 #msc:14C30 #msc:14C40 #msc:14G40 #msc:14K20 #msc:14K22
paper · pdf · doi:10.48550/arxiv.math/0209177
20 pages, submitted
arxiv created 2002/09/14 · arxiv updated 2009/11/30
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.