An effective result of André-Oort type II

Lars Kühne

An effective result of André-Oort type II

Lars Kühne

Acta Arithmetica (2013)

Volume: 161, Issue: 1, page 1-19
ISSN: 0065-1036

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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.

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Lars Kühne. "An effective result of André-Oort type II." Acta Arithmetica 161.1 (2013): 1-19. <http://eudml.org/doc/286622>.

@article{LarsKühne2013,
abstract = {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.},
author = {Lars Kühne},
journal = {Acta Arithmetica},
keywords = {André-Oort conjecture; modular curve; effective; uniformity},
language = {eng},
number = {1},
pages = {1-19},
title = {An effective result of André-Oort type II},
url = {http://eudml.org/doc/286622},
volume = {161},
year = {2013},
}

TY - JOUR
AU - Lars Kühne
TI - An effective result of André-Oort type II
JO - Acta Arithmetica
PY - 2013
VL - 161
IS - 1
SP - 1
EP - 19
AB - 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.
LA - eng
KW - André-Oort conjecture; modular curve; effective; uniformity
UR - http://eudml.org/doc/286622
ER -

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