A Geometric Analogue of the Birch and Swinnerton-Dyer Conjecture over the Complex Number Field

Sugiyama, Ken-ichi

J. Differential Geom., Tome 66 (2004) no. 3, p. 73-98 / Harvested from Project Euclid

Résumé

We will define a Ruelle–Selberg type zeta function for a certain lomathcal system over a Riemann surface whose genus is greater than or equal to three. Also we will investigate its property, especially their special values. As an application, we will show that a geometric analogue of BSD conjecture is true for a family of abelian varieties which has only semi-stable reductions defined over the complex number field.

Publié le : 2004-09-14
Classification:

@article{1102536710,
     author = {Sugiyama, Ken-ichi},
     title = {A Geometric Analogue of the Birch and Swinnerton-Dyer Conjecture over the Complex Number Field},
     journal = {J. Differential Geom.},
     volume = {66},
     number = {3},
     year = {2004},
     pages = { 73-98},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1102536710}
}

Sugiyama, Ken-ichi. A Geometric Analogue of the Birch and Swinnerton-Dyer Conjecture over the Complex Number Field. J. Differential Geom., Tome 66 (2004) no. 3, pp.  73-98. http://gdmltest.u-ga.fr/item/1102536710/