An effective result of André-Oort type II

• Autorzy: Lars Kühne
• Języki publikacji: EN

Abstrakty

EN

We prove some new effective results of André-Oort type. In particular, we state certain uniform improvements of the main result in [L. Kühne, Ann. of Math. 176 (2012), 651-671]. We also show that the equation X + Y = 1 has no solution in singular moduli. As a by-product, we indicate a simple trick rendering André's proof of the André-Oort conjecture effective. A significantly new aspect is the usage of both the Siegel-Tatuzawa theorem and the weak effective lower bound on the class number of an imaginary quadratic field given by Gross and Zagier. The results of this article were partially announced in the above-cited paper.

Kategorie tematyczne

• 14G05: Rational points
• 11G18: Arithmetic aspects of modular and Shimura varieties
• 14G35: Modular and Shimura varieties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 161
• Numer: 1
• Strony: 1-19

Daty

wydano

2013

Twórcy

autor

Lars Kühne

• SNS Pisa, Piazza dei Cavalieri 7, 56126 Pisa, Italy

Identyfikatory

DOI

10.4064/aa161-1-1