On the torsion of Drinfeld modules of rank two
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.
© Walter de Gruyter Berlin · New York 2010
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- On the torsion of Drinfeld modules of rank two
- Endpoint maximal and smoothing estimates for Schrödinger equations
- Kähler-Ricci flow on stable Fano manifolds
- Area-minimizing vector fields on round 2-spheres
- Koppelman formulas on Grassmannians
- A quotient restriction theorem for actions of real reductive groups
- Graph algebras, Exel-Laca algebras, and ultragraph algebras coincide up to Morita equivalence
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Articles in the same Issue
- On the torsion of Drinfeld modules of rank two
- Endpoint maximal and smoothing estimates for Schrödinger equations
- Kähler-Ricci flow on stable Fano manifolds
- Area-minimizing vector fields on round 2-spheres
- Koppelman formulas on Grassmannians
- A quotient restriction theorem for actions of real reductive groups
- Graph algebras, Exel-Laca algebras, and ultragraph algebras coincide up to Morita equivalence
- On the bounded cohomology of semi-simple groups, S-arithmetic groups and products
- Über Pro-p-Fundamentalgruppen markierter arithmetischer Kurven
