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.
Paga facilmente con carta, Klarna, Apple Pay o Google Pay. Non sei soddisfatto? Hai sempre 14 giorni per il rimborso. Leggi di più nei nostri termini. Per qualsiasi domanda, scrivici a hello@memmo.org.
Memmo rende lo studio più facile, ovunque tu sia nel mondo. Qui trovi i tuoi libri di testo e strumenti di studio intelligenti, tutto in un unico posto: riassunti, quiz, podcast e flashcard. E poi c'è Ted, il tuo compagno di studio che risponde a ogni tua domanda. Oltre 50.000 studenti studiano già qui: è stato creato per aiutarti a imparare più velocemente e a stressarti meno.