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The Gross-Zagier Formula on Shimura Curves - 9780691155920
Un libro in lingua di Xinyi Yuan Shou-Wu Zhang Wei Zhang edito da Princeton Univ Pr, 2012
- € 91.70
- Il prezzo è variabile in funzione del cambio della valuta d’origine
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.
Informazioni bibliografiche
- Titolo del Libro in lingua: The Gross-Zagier Formula on Shimura Curves
- Lingua: English
- Autori : Xinyi Yuan Shou-Wu Zhang Wei Zhang
- Editore: Princeton Univ Pr
- Collana: Princeton Univ Pr (Paperback)
- Data di Pubblicazione: 12 Novembre '12
- Genere: MATHEMATICS
- Argomenti : Shimura varieties Arithmetical algebraic geometry Automorphic forms
- Pagine: 256
- Dimensioni mm: 228 x 152 x 0
- ISBN-10: 0691155925
- EAN-13: 9780691155920