Title: A function field analogue of the Rasmussen-Tamagawa conjecture: The Drinfeld module case,
Abstract: In the arithmetic of function fields, Drinfeld modules play the role that
elliptic curves play in the arithmetic of number fields. The aim of this paper
is to study a non-existence problem of Drinfeld modules with constrains on
torsion points at places with large degree. This is motivated by a conjecture
of Christopher Rasmussen and Akio Tamagawa on the non-existence of abelian
varieties over number fields with some arithmetic constraints. We prove the
non-existence of Drinfeld modules satisfying Rasmussen-Tamagawa type conditions
in the case where the inseparable degree of base fields is not divisible by the
rank of Drinfeld modules. Conversely if the rank divides the inseparable
degree, then we give an example of Drinfeld modules satisfying
Rasmussen-Tamagawa-type conditions.