The Gross-Zagier formula on Shimura curves

The Resource The Gross-Zagier formula on Shimura curves
Label
The Gross-Zagier formula on Shimura curves
Statement of responsibility
Xinyi Yuan, Shou-wu Zhang, and Wei Zhang
Creator
Contributor
Subject
Language
eng
Summary
"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
Member of
Cataloging source
DLC
Index
index present
Literary form
non fiction
Nature of contents
bibliography
Series statement
Annals of mathematics studies
Series volume
no. 184

Context

Context of The Gross-Zagier formula on Shimura curves

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