Algebraic independence of periods of Anderson modules and their hyperderivatives

@misc{maurischat2026algebraic,
  title = {{Algebraic independence of periods of Anderson modules and their hyperderivatives}},
  author = {Andreas Maurischat and Changningphaabi Namoijam},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.24699},
  eprint = {2609.24699},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24699},
}

TY  - UNPB
TI  - Algebraic independence of periods of Anderson modules and their hyperderivatives
AU  - Andreas Maurischat
AU  - Changningphaabi Namoijam
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.24699
UR  - https://arxiv.org/abs/2609.24699
AB  - Transcendence questions of periods and quasi-periods of Anderson modules, as well as the hyperderivatives thereof, are of major interest in number theory over function fields. In the case of Drinfeld modules, this question was answered by the second author. In this paper, we show that these results hold for general Anderson t-modules under certain assumptions on their Galois representations. The proofs use the explicit description of the p-adic Galois representation of the first author by means of a rigid analytic trivialization of the associated t-motive, as well as prolongations of t-modules and t-motives. The general result is applied to determine algebraic relations between periods and quasi-periods, and their hyperderivatives, of finitely many Drinfeld modules. Along the way, our results provide more evidence for the Mumford-Tate conjecture for Anderson modules.
ER  -