The Gross-Zagier formula on Shimura curves /
Yuan, Xinyi, 1981-
The Gross-Zagier formula on Shimura curves / Xinyi Yuan, Shou-wu Zhang, and Wei Zhang. - Princeton : Princeton University Press, 2012, ©2013. - 1 online resource (viii, 256 pages) - Annals of mathematics studies ; no. 184 . - Annals of mathematics studies ; no. 184. .
Includes bibliographical references and index.
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.
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.
9781400845644 (electronic bk.) 1400845645 (electronic bk.) 0691155925 9780691155920 0691155917 (hardcover ; alk. paper) 9780691155913 (hardcover ; alk. paper) (hardcover ; alk. paper) (pbk. ; alk. paper)
10.1515/9781400845644 doi
22573/cttjzjgz JSTOR
016162248 Uk
Shimura varieties.
Arithmetical algebraic geometry.
Automorphic forms.
Quaternions.
Variétés de Shimura.
Géométrie algébrique arithmétique.
Formes automorphes.
Quaternions.
MATHEMATICS--Geometry--Algebraic.
Arithmetical algebraic geometry.
Automorphic forms.
Quaternions.
Shimura varieties.
Electronic books.
Electronic books.
QA242.5 / .Y83 2012eb
516.3/52
The Gross-Zagier formula on Shimura curves / Xinyi Yuan, Shou-wu Zhang, and Wei Zhang. - Princeton : Princeton University Press, 2012, ©2013. - 1 online resource (viii, 256 pages) - Annals of mathematics studies ; no. 184 . - Annals of mathematics studies ; no. 184. .
Includes bibliographical references and index.
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.
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.
9781400845644 (electronic bk.) 1400845645 (electronic bk.) 0691155925 9780691155920 0691155917 (hardcover ; alk. paper) 9780691155913 (hardcover ; alk. paper) (hardcover ; alk. paper) (pbk. ; alk. paper)
10.1515/9781400845644 doi
22573/cttjzjgz JSTOR
016162248 Uk
Shimura varieties.
Arithmetical algebraic geometry.
Automorphic forms.
Quaternions.
Variétés de Shimura.
Géométrie algébrique arithmétique.
Formes automorphes.
Quaternions.
MATHEMATICS--Geometry--Algebraic.
Arithmetical algebraic geometry.
Automorphic forms.
Quaternions.
Shimura varieties.
Electronic books.
Electronic books.
QA242.5 / .Y83 2012eb
516.3/52