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The Gross-Zagier formula on Shimura curves /
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....
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton :
Princeton University Press,
2012, ©2013.
|
| Colección: | Annals of mathematics studies ;
no. 184. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 082 | 0 | 4 | |a 516.3/52 |2 23 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Yuan, Xinyi, |d 1981- | |
| 245 | 1 | 4 | |a The Gross-Zagier formula on Shimura curves / |c Xinyi Yuan, Shou-wu Zhang, and Wei Zhang. |
| 260 | |a Princeton : |b Princeton University Press, |c 2012, ©2013. | ||
| 300 | |a 1 online resource (viii, 256 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Annals of mathematics studies ; |v no. 184 | |
| 504 | |a Includes bibliographical references and index. | ||
| 520 | |a 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. | ||
| 505 | 0 | 0 | |t Frontmatter -- |t Contents -- |t Preface -- |t Chapter One. Introduction and Statement of Main Results -- |t Chapter Two. Weil Representation and Waldspurger Formula -- |t Chapter Three. Mordell-Weil Groups and Generating Series -- |t Chapter Four. Trace of the Generating Series -- |t Chapter Five. Assumptions on the Schwartz Function -- |t Chapter Six. Derivative of the Analytic Kernel -- |t Chapter Seven. Decomposition of the Geometric Kernel -- |t Chapter Eight. Local Heights of CM Points -- |t Bibliography -- |t Index. |
| 546 | |a In English. | ||
| 590 | |a JSTOR |b Books at JSTOR All Purchased | ||
| 590 | |a JSTOR |b Books at JSTOR Demand Driven Acquisitions (DDA) | ||
| 590 | |a JSTOR |b Books at JSTOR Evidence Based Acquisitions | ||
| 650 | 0 | |a Shimura varieties. | |
| 650 | 0 | |a Arithmetical algebraic geometry. | |
| 650 | 0 | |a Automorphic forms. | |
| 650 | 0 | |a Quaternions. | |
| 650 | 6 | |a Variétés de Shimura. | |
| 650 | 6 | |a Géométrie algébrique arithmétique. | |
| 650 | 6 | |a Formes automorphes. | |
| 650 | 6 | |a Quaternions. | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x Algebraic. |2 bisacsh | |
| 650 | 7 | |a Arithmetical algebraic geometry |2 fast | |
| 650 | 7 | |a Automorphic forms |2 fast | |
| 650 | 7 | |a Quaternions |2 fast | |
| 650 | 7 | |a Shimura varieties |2 fast | |
| 700 | 1 | |a Zhang, Shouwu. | |
| 700 | 1 | |a Zhang, Wei, |d 1981- | |
| 776 | 0 | 8 | |i Print version: |a Yuan, Xinyi, 1981- |t Gross-Zagier formula on Shimura curves. |d Princeton : Princeton University Press, 2012, ©2013 |w (DLC) 2012010981 |
| 830 | 0 | |a Annals of mathematics studies ; |v no. 184. | |
| 856 | 4 | 0 | |u https://jstor.uam.elogim.com/stable/10.2307/j.cttq94r3 |z Texto completo |
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