Florian Breuer
Titel: Torsion bounds for elliptic curves and Drinfeld modules
Abstract: Let E/K be an elliptic curve defined over a finitely
generated field of characteristic zero. I will show that for any
finite extension L/K, the number of L-rational torsion points of E is
bounded by C([L:K]log log [L:K])^e, where e=1 if E has complex
multiplication, and e=1/2 otherwise. C is a constant depending on
E/K.This bound is best possible, in the sense that there is a tower of
field extensions L which achieves this bound for sufficiently small C.
I will also show a similar result for Drinfeld modules. In fact the
argument (which is a simple application of the adelic openness of the
associated Galois representations) can be applied simultaneously to
elliptic curves and Drinfeld modules.