The André-Oort conjecture for Drinfeld modular varieties

• Verfasst von: Hubschmid, Patrik [VerfasserIn]
• Titel: The André-Oort conjecture for Drinfeld modular varieties
• Verf.angabe: Patrik Hubschmid
• E-Jahr: 2013
• Jahr: 14 February 2013
• Umfang: 61 S.
• Fussnoten: Gesehen am 05.01.2022
• Titel Quelle: Enthalten in: Compositio mathematica
• Ort Quelle: Cambridge : Cambridge Univ. Press, 1935
• Jahr Quelle: 2013
• Band/Heft Quelle: 149(2013), 4, Seite 507-567
• ISSN Quelle: 1570-5846
• DOI: doi:10.1112/S0010437X12000681
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: 11G09
• Sach-SW: 14G35
• Sach-SW: André-Oort conjecture
• Sach-SW: Drinfeld modular varieties
• K10plus-PPN: 1784824062

Abstract

We consider the analogue of the André-Oort conjecture for Drinfeld modular varieties which was formulated by Breuer. We prove this analogue for special points with separable reflex field over the base field by adapting methods which were used by Klingler and Yafaev to prove the André-Oort conjecture under the generalized Riemann hypothesis in the classical case. Our result extends results of Breuer showing the correctness of the analogue for special points lying in a curve and for special points having a certain behaviour at a fixed set of primes.