## Some remarks on the reduction map for Drinfeld modules

### Volume 210 / 2023

Acta Arithmetica 210 (2023), 175-190
MSC: Primary 11G09; Secondary 14G05, 14G25, 11J93.
DOI: 10.4064/aa220801-6-7
Published online: 28 July 2023

#### Abstract

In the paper by W. Bondarewicz and the author [Acta Arith. 195 (2020)] a sufficient condition for the local to global principle for Anderson ${\bf t}$-modules that are products $\widehat \varphi =\phi _{1}^{e_{1}}\times \dots \times \phi _{t}^{e_{t}}$ of non-isogenous Drinfeld modules was established. The Drinfeld modules $\phi _i$ were assumed to have trivial endomorphism rings, i.e. ${\rm End}_{K^{\rm sep}}(\phi _i)=A=\mathbb F_q[t].$ In this paper we prove a variant of the local to global principle for Drinfeld modules with the endomorphism ring not necessarily equal to $A$.