Vai al contenuto principale della pagina
Autore: |
Yuan Xinyi <1981->
![]() |
Titolo: |
The Gross-Zagier formula on Shimura curves / / Xinyi Yuan, Shou-wu Zhang, and Wei Zhang
![]() |
Pubblicazione: | Princeton, : Princeton University Press, 2012, c2013 |
Edizione: | Course Book |
Descrizione fisica: | 1 online resource (267 p.) |
Disciplina: | 516.3/52 |
Soggetto topico: | Shimura varieties |
Arithmetical algebraic geometry | |
Automorphic forms | |
Quaternions | |
Altri autori: |
ZhangShouwu
![]() ![]() |
Note generali: | Description based upon print version of record. |
Nota di bibliografia: | Includes bibliographical references and index. |
Nota di contenuto: | 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 |
Sommario/riassunto: | 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. This is followed by a complete proof of its coherent analogue: the Waldspurger formula, which relates the periods of integrals and the special values of L-series by means of Weil representations. The Gross-Zagier formula is then reformulated in terms of incoherent Weil representations and Kudla's generating series. Using Arakelov theory and the modularity of Kudla's generating series, the proof of the Gross-Zagier formula is reduced to local formulas. The Gross-Zagier Formula on Shimura Curves will be of great use to students wishing to enter this area and to those already working in it. |
Titolo autorizzato: | The Gross-Zagier formula on Shimura curves ![]() |
ISBN: | 9786613883919 |
1-4008-4564-5 | |
1-283-57146-3 | |
Formato: | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione: | Inglese |
Record Nr.: | 9910817785603321 |
Lo trovi qui: | Univ. Federico II |
Opac: | Controlla la disponibilità qui |