On the Torsion of Drinfeld Modules of Rank Two
نویسندگان
چکیده
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 general 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.
منابع مشابه
Ranks of modules relative to a torsion theory
Relative to a hereditary torsion theory $tau$ we introduce a dimension for a module $M$, called {em $tau$-rank of} $M$, which coincides with the reduced rank of $M$ whenever $tau$ is the Goldie torsion theory. It is shown that the $tau$-rank of $M$ is measured by the length of certain decompositions of the $tau$-injective hull of $M$. Moreover, some relations between the $tau$-rank of $M$ and c...
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