Neron-Tate heights on algebraic curves and subgroups of the modular group

Ulf Kühn

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2001-12, 23 pages

MSC 2000

14G40 Arithmetic varieties and schemes; Arakelov theory; heights
11F66 Dirichlet series and functional equations in
11G40 $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture

We give an expression for the value of the Neron-Tate height pairing of two divisors on an algebraic curve which involves special values of certain Dirichlet series associated to finite index subgroups of the modular group.

Keywords:Neron-Tate heights, Arakelov geometry, modular curves, Eisenstein series, scattering matrix, noncongruence subgroups