Abstract
We prove that the curve Y0(𝔭) has no 𝔽2(T)-rational points where 𝔭 ⊲ 𝔽2[T] is a prime ideal of degree at least 3 and Y0(𝔭) is the affine Drinfeld modular curve parameterizing Drinfeld modules of rank two over 𝔽2[T] of generic characteristic with Hecke-type level 𝔭-structure. As a consequence we derive a conjecture of Schweizer describing completely the torsion of Drinfeld modules of rank two over 𝔽2(T) implying the uniform boundedness conjecture in this particular case. We reach our results with a variant of the formal immersion method. Moreover we show that the group Aut(X0(𝔭)) has order two. As a further application of our methods we also determine the prime-to-p cuspidal torsion packet of X0(𝔭) where 𝔭 ⊲ 𝔽q[T] is a prime ideal of degree at least 3 and q is a power of the prime p.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal für die reine und angewandte Mathematik (Crelles Journal)
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
