C\'ecile Armana
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Titel: "Rational torsion of rank-2 Drinfeld modules"
Abstract:
It is known since 1994 that the order of a torsion point of an elliptic
curve over a number field of degree $d$ is bounded by constant depending
only on $d$. The proof, due to Mazur, Kamienny and finally Merel, is a
study of rational points on classical modular curves. A similar uniform
boundedness conjecture has been stated by Poonen for Drinfeld modules in
1997. In this talk, we will discuss to what extent the classical proof
applies to rank-$2$ Drinfeld modules over function fields. Under a
hypothesis on the Hecke structure of Drinfeld modular forms, we obtain a
result towards the conjecture. We also prove that there is no rational
torsion of small degree.