The Gross-Zagier formula on Shimura curves / Xinyi Yuan, Shou-wu Zhang, and Wei Zhang.

By:

Yuan, Xinyi, 1981-

Contributor(s):

Material type: Text

text

Media type:

computer

Carrier type:

online resource

ISBN:

9781400845644
1400845645
0691155925
9780691155920
0691155917
9780691155913

Subject(s): Genre/Form:

Additional physical formats: Print version:: Gross-Zagier formula on Shimura curves.DDC classification:

516.3/52 23

LOC classification:

QA242.5 .Y83 2012eb

Online resources:

Click here to access online

Contents:

Frontmatter -- Contents -- Preface -- Chapter One. Introduction and Statement of Main Results -- Chapter Two. Weil Representation and Waldspurger Formula -- Chapter Three. Mordell-Weil Groups and Generating Series -- Chapter Four. Trace of the Generating Series -- Chapter Five. Assumptions on the Schwartz Function -- Chapter Six. Derivative of the Analytic Kernel -- Chapter Seven. Decomposition of the Geometric Kernel -- Chapter Eight. Local Heights of CM Points -- Bibliography -- Index.

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.

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Includes bibliographical references and index.

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.

In English.

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