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arXiv · 2607.26233

On purity of Anderson t-modules

Yen-Tsung Chen·Andreas Maurischat
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Abstract

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.

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Yen-Tsung Chen, Andreas Maurischat. 2026-07-28. On purity of Anderson t-modules. https://arxiv.org/abs/2607.26233

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