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The Gross-Zagier Formula on Shimura Curves

Af: Wei Zhang, Xinyi Yuan, Shou-wu Zhang Engelsk Paperback

The Gross-Zagier Formula on Shimura Curves

Af: Wei Zhang, Xinyi Yuan, Shou-wu Zhang Engelsk Paperback
Tjek vores konkurrenters priser

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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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.

Produktdetaljer
Sprog: Engelsk
Sider: 272
ISBN-13: 9780691155920
Indbinding: Paperback
Udgave:
ISBN-10: 0691155925
Udg. Dato: 2 dec 2012
Længde: 13mm
Bredde: 157mm
Højde: 234mm
Forlag: Princeton University Press
Oplagsdato: 2 dec 2012
Forfatter(e) Wei Zhang, Xinyi Yuan, Shou-wu Zhang


Kategori Algebraisk geometri


ISBN-13 9780691155920


Sprog Engelsk


Indbinding Paperback


Sider 272


Udgave


Længde 13mm


Bredde 157mm


Højde 234mm


Udg. Dato 2 dec 2012


Oplagsdato 2 dec 2012


Forlag Princeton University Press

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