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- Title
On the torsion of Drinfeld modules of rank two.
- Authors
Pál, Ambrus
- Abstract
We prove that the curve Y0() has no 2( T)-rational points where ⊲ 2[ T] is a prime ideal of degree at least 3 and Y0() is the affine Drinfeld modular curve parameterizing Drinfeld modules of rank two over 2[ T] of generic characteristic with Hecke-type level -structure. As a consequence we derive a conjecture of Schweizer describing completely the torsion of Drinfeld modules of rank two over 2( 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()) has order two. As a further application of our methods we also determine the prime-to- p cuspidal torsion packet of X0() where ⊲ q[ T] is a prime ideal of degree at least 3 and q is a power of the prime p.
- Subjects
CURVES; DRINFELD modules; MODULES (Algebra); BOUNDARY value problems; TORSION products; TORSION theory (Algebra)
- Publication
Journal für die Reine und Angewandte Mathematik, 2010, Vol 2010, Issue 640, p1
- ISSN
0075-4102
- Publication type
Article
- DOI
10.1515/CRELLE.2010.017