Xinyi Yuan, Shou-Wu Zhang, Wei Zhang

The Gross-Zagier Formula on Shimura Curves

• Broschiertes Buch

Produktbeschreibung

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.

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Produktdetails

• Verlag: Princeton University Press
• Seitenzahl: 268
• Erscheinungstermin: 2. Dezember 2012
• Englisch
• Abmessung: 234mm x 156mm x 15mm
• Gewicht: 412g
• ISBN-13: 9780691155920
• ISBN-10: 0691155925
• Artikelnr.: 35940330

Autorenporträt

Xinyi Yuan is assistant professor of mathematics at Princeton University. Shou-wu Zhang is professor of mathematics at Princeton University and Columbia University. Wei Zhang is assistant professor of mathematics at Columbia University.