Notice bibliographique
- Notice
Type(s) de contenu et mode(s) de consultation : Texte noté : sans médiation
Auteur(s) : Yuan, Xin yi (1981-....)
Zhang, Shou wu (1962-....)
Zhang, Wei (1981-....)
Titre(s) : The Gross-Zagier formula on Shimura curves [Texte imprimé] / Xinyi Yuan, Shou-wu Zhang, and Wei Zhang
Publication : Princeton (N.J.) : Princeton university press, cop. 2013
Description matérielle : 1 vol. (VI-256 p.) ; 25 cm
Collection : Annals of mathematics studies ; Nr. 184
Lien à la collection : Annals of mathematics studies
Comprend : Introduction and Statement of Main Results ; Weil Representation and Waldspurger Formula
; Mordell-Weil Groups and Generating Series ; Trace of the Generating Series ;
Assumptions on the Schwartz Function ; Derivative of the Analytic Kernel ; Decomposition
of the Geometric Kernel ; Local Heights of CM Points.
Note(s) : Bibliogr. p. 252-254
"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."--Publisher's website
Sujet(s) : Shimura, Variétés de
Quaternions
Automorphismes
Indice(s) Dewey :
512.5 (23e éd.) = Algèbre linéaire ; 516.352 (23e éd.) = Courbes et surfaces sur des plans projectifs et affines
Identifiants, prix et caractéristiques : ISBN 9780691155913. - ISBN 0691155917 (rel.). - ISBN 9780691155920. - ISBN 0691155925
(br.)
Identifiant de la notice : ark:/12148/cb427603690
Notice n° :
FRBNF42760369
(notice reprise d'un réservoir extérieur)
