On Drinfeld modules with Rasmussen-Tamagawa type conditions: a resume (Algebraic Number Theory and Related Topics 2017)

Abstract

This is an announcement of the author's results [7] on a non-existence problem of Drinfeld modules defined over global function fields with some arithmetic constraints. The motivation is a conjecture of Christopher Rasmussen and Akio Tamagawa related with abelian varieties over number fields with constrained ℓ-power torsion points. In this paper, considering the arithmetic similarity between Drinfeld modules and elliptic curves, we show that a Drinfeld module analogue of the Rasmussen-Tamagawa conjecture holds in some cases. We also see that there is a counter-example of the Drinfeld module analogue of the conjecture in a special case.