2026/07/28 by Yen-Tsung Chen, Andreas Maurischat
Mathematics · #math.NT #math.RA #msc:11G09 #msc:15A23 #msc:16S36 #msc:16W60
24 pages
arxiv created 2026/07/28 · arxiv updated 2026/07/30
In the theory of abelian Anderson t-modules, pure Anderson t-modules play an important role. Namoijam and Papanikolas also introduced the notions of strictly pure and almost strictly pure t-modules which are special classes of pure t-modules. Whereas it is well known that not all pure t-modules are isomorphic to strictly pure ones (e.g.~the tensor powers of the Carlitz module), the same question for almost strictly pure t-modules was not answered yet. In this article, we show that every pure Anderson t-module defined over a field K is indeed isomorphic to an almost strictly pure Anderson t-module after base change to a suitable finite algebraic extension of K. We also give a necessary and sufficient criterion when such an isomorphism to a strictly pure Anderson t-module is possible.