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Princeton University Press - The Gross-Zagier Formula on Shimura Curves

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Description

Explore a deep mathematical study with The Gross-Zagier Formula on Shimura Curves, part of the Annals of Mathematics Studies series (AMS-184). Published by Princeton University Press, this text provides a comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields. This work connects the heights of Heegner points on abelian varieties to the derivatives of L-series. Such connections provide new applications for the Birch and Swinnerton-Dyer conjecture and various Diophantine equations. The text begins with a conceptual formulation of the formula using incoherent quaternion algebras and incoherent automorphic representations with rational coefficients. These coefficients are attached naturally to abelian varieties parametrized by Shimura curves. This volume serves as a detailed resource for those studying advanced geometry, topology, and number theory.

Key Features

Provides a 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.

Offers new applications for the Birch and Swinnerton-Dyer conjecture and Diophantine equations.

Includes a conceptual formulation using incoherent quaternion algebras and automorphic representations.

Part of the prestigious Annals of Mathematics Studies series, volume 184.

Covers abelian varieties parametrized by Shimura curves with natural rational coefficients.

Product Specifications

Format
hardcover
Domain
Amazon UK
Release Date
04 January 2013
Listed Since
24 April 2012

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