The length of the tail of affine equations of Drinfeld modules and their duals

A. Grishkov, D. Logachev

Published 2023-02-27Version 1

The authors defined in "$h^1\ne h_1$ for Anderson t-motives" ([GL21]) the notion of an affine equation associated to a t-motive $M$, and conjectured that the length of its tail is $n$ -- the dimension of $M$. This conjecture was checked in [GL21] for some t-motives of ranks $r=4$ and 5, and of $n=2$. We show in the present paper that it is true for Drinfeld modules and their duals. Since the dimension of the dual of a Drinfeld module of rank $r$ is $r-1$, this is the first checking of this conjecture for $n>2$.