On height functions on Jacobian surfaces | Zendy

Kentaro Yoshitomi | Zendy

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On height functions on Jacobian surfaces

Author(s) -

Kentaro Yoshitomi

Publication year - 1998

Publication title -

manuscripta mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.752

H-Index - 46

eISSN - 1432-1785

pISSN - 0025-2611

DOI - 10.1007/s002290050053

Subject(s) - jacobian matrix and determinant , mathematics , algebraic geometry , number theory , surface (topology) , abelian group , pure mathematics , group (periodic table) , arithmetic of abelian varieties , shimura variety , mathematical analysis , modular form , geometry , elementary abelian group , rank of an abelian group , physics , quantum mechanics

The canonical height on an abelian variety is useful and important for the study of the Mordell-Weil group. But it is difficult to calculate the canonical height in general. We give an effective method to calculate the canonical height on a Jacobian surface. As an application, we verify the Birch-Swinnerton-Dyer conjecture for the Jacobian surface of a twisted modular curve.

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