A fixed point formula of Lefschetz type in Arakelov geometry IV: The modular height of C.M. abelian varieties
| Autor: | Kai Köhler, Damian Roessler |
|---|---|
| Rok vydání: | 2003 |
| Předmět: |
Abelian variety
Mathematics - Differential Geometry Applied Mathematics General Mathematics Mathematics::Number Theory 14K22 Abelian extension Geometry Elementary abelian group 58G10 58G26 Rank of an abelian group 14G40 Faltings height Mathematics - Algebraic Geometry 11M06 Differential Geometry (math.DG) Abelian variety of CM-type FOS: Mathematics Abelian group Algebraic Geometry (math.AG) Mathematics Arithmetic of abelian varieties |
| Zdroj: | Journal für die reine und angewandte Mathematik. 2003(556) |
| ISSN: | 0075-4102 1435-5345 |
| Popis: | 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. Comment: 25 pages |
| Databáze: | OpenAIRE |
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