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September 2004 A Geometric Analogue of the Birch and Swinnerton-Dyer Conjecture over the Complex Number Field
Ken-ichi Sugiyama
J. Differential Geom. 68(1): 73-98 (September 2004). DOI: 10.4310/jdg/1102536710

Abstract

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.

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Ken-ichi Sugiyama. "A Geometric Analogue of the Birch and Swinnerton-Dyer Conjecture over the Complex Number Field." J. Differential Geom. 68 (1) 73 - 98, September 2004. https://doi.org/10.4310/jdg/1102536710

Information

Published: September 2004
First available in Project Euclid: 8 December 2004

zbMATH: 1099.11047
MathSciNet: MR2152909
Digital Object Identifier: 10.4310/jdg/1102536710

Rights: Copyright © 2004 Lehigh University

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Vol.68 • No. 1 • September 2004
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