"Formas automórficas." . . "Cuaterniones." . . "Formes automorphes." . . "Shimura varieties." . . "Shimura varieties" . "MATHEMATICS / Geometry / Algebraic" . . "Geometría algebraica." . . "Quaternions." . . "Quaternions" . . . "Arithmetical algebraic geometry." . . "Arithmetical algebraic geometry" . "Géométrie algébrique arithmétique." . . "Formes automòrfiques." . . "Variétés de Shimura." . . "Automorphic forms." . . "Automorphic forms" . "Varietats de Shimura." . . "Shimura, Variétés de." . . . . . . . . . "The Gross-Zagier formula on Shimura curves"@en . "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. 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." . . . . . . . . "Gross-Zagier formula on Shimura curves" . . . . . . "Electronic books"@en . . . . . . . . "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 o."@en . . . . . . . . "Geometria algebraica aritmètica." . . "Shimura, Variedades de." . .