The Gross-Zagier Formula on Shimura Curves
Course Book. - Princeton, NJ: Princeton University Press, [2012]
Online
Monographie, Elektronische Ressource
- 1 online resource
Ermittle Ausleihstatus...
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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The Gross-Zagier Formula on Shimura Curves
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Verantwortlichkeitsangabe: | Wei Zhang, Shou-wu Zhang, Xinyi Yuan |
Autor/in / Beteiligte Person: | Yuan, Xinyi ; Zhang, Shou-wu ; Zhang, Wei |
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Ausgabe: | Course Book |
Veröffentlichung: | Princeton, NJ: Princeton University Press, [2012] |
Medientyp: | Monographie |
Datenträgertyp: | Elektronische Ressource |
Umfang: | 1 online resource |
ISBN: | 9781400845644 |
DOI: | 10.1515/9781400845644 |
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