For each positive characteristic multiple zeta value (defined by Thakur) , Chang-Papanikolas-Yu constructed the -module defined over and integral points , . They proved that is Eulerian (resp. zeta-like) if and only if is an -torsion point in (resp. , are -linearly dependent in ).

 

In this talk, we are interested in the structure theory of the -module . Poonen proved an analogue for Drinfeld modules of the Mordell-Weil theorem. We shall generalize his results to the case of specific families of -modules. In particular, we prove that the -module is the direct sum of its torsion submodule, which is finite, with a free -module of rank .