2001/05/11 by Kai Koehler, Koehler, Kai, Damian Roessler +1
Computer Science · Mathematics · #11M06 #14G40 #14K22 #58G10 #58G26 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Differential Geometry (math.DG) #FOS: Mathematics #Polynomial and algebraic computation #math.AG #math.DG #msc:11M06 #msc:14G40 #msc:14K22 #msc:58G10 #msc:58G26
paper · pdf · doi:10.48550/arxiv.math/0105101
25 pages
arxiv created 2001/05/11 · openalex publication_date 2001/05/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a new proof of a slightly weaker form of a theorem of P. Colmez. This theorem gives a formula for the Faltings height of abelian varieties with complex multiplication by a C.M. field whose Galois group over \bf Q is abelian; it reduces to the formula of Chowla and Selberg in the case of elliptic curves. We show that the formula can be deduced from the arithmetic fixed point formula proved in the first paper of the series. Our proof is intrinsic in the sense that it does not rely on the computation of the periods of any particular abelian variety.