The Gross-Zagier Formula on Shimura Curves (Annals of Mathematics Studies): (AMS-184) - Image 1

£45.84

Princeton University Press The Gross-Zagier Formula on Shimura Curves (Annals of Mathematics Studies): (AMS-184)

Name: The Gross-Zagier Formula on Shimura Curves (Annals of Mathematics Studies): (AMS-184)
Brand: Princeton University Press
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Geometry & Topology

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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.

Product Specifications

Brand: Princeton University Press
Format: paperback
ASIN: 0691155925
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Geometry & Topology
Domain: Amazon UK
Release Date: 02 December 2012
Listed Since: 24 April 2012

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Princeton University Press The Gross-Zagier Formula on Shimura Curves (Annals of Mathematics Studies): (AMS-184)

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