The Gross-Zagier Formula on Shimura Curves : (AMS-184) /

This comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. The formula will have new applications for the Birch and Swinnerton-Dyer conjecture and Diophantine equations....

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Bibliographic Details
Main Author: Yuan, Xinyi, 1981-
Other Authors: Zhang, Wei, 1981-, Zhang, Shouwu
Format: Electronic eBook
Language:Inglés
Published: Princeton : Princeton University Press, 2012, 2013.
Series:Book collections on Project MUSE.
Subjects:
Shimura varieties.
Quaternions.
Automorphic forms.
Arithmetical algebraic geometry.
MATHEMATICS > Geometry > Algebraic.
Formes automorphes.
Geometrie algebrique arithmetique.
Varietes de Shimura.
Electronic books.
Online Access:Texto completo
Description
Summary:This comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. The formula will have new applications for the Birch and Swinnerton-Dyer conjecture and Diophantine equations. The book begins with a conceptual formulation of the Gross-Zagier formula in terms of incoherent quaternion algebras and incoherent automorphic representations with rational coefficients attached naturally to abelian varieties parametrized by Shimura curves.
Physical Description:1 online resource.
ISBN:9781400845644

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