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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2512.07607 |
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| _version_ | 1866912754129960960 |
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| author | Kędzierski, Dawid E. Krasoń, Piotr |
| author_facet | Kędzierski, Dawid E. Krasoń, Piotr |
| contents | We introduce and study a natural class of Anderson t- modules, called triangular t-modules, characterized by having Drinfeld modules as their $τ$-composition factors. They form a homologically meaningful generalization of Drinfeld modules and exhibit rich arithmetic structure.\smallskip
We establish criteria for purity, strict and almost strict, and develop a reduction procedure that lowers the degrees of the defining biderivations. As a consequence, every almost strictly pure triangular t-module becomes strictly pure after a finite base extension.
We then investigate morphisms and isogenies between triangular t-modules, provide a characterization of triangular isogenies, and describe the algebra of endomorphisms, including a criterion for commutativity. On the analytic side, we show that all triangular t- modules are uniformizable and establish finiteness and purity criteria with consequences for Taelman's conjecture.
Finally, we develop a duality theory for triangular t- modules and their biderivations, proving compatibility with $τ$-composition series and establishing analogues of the Cartier-Nishi theorem and the Weil-Barsotti formula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07607 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homological Methods in the Generalization of Drinfeld Modules Kędzierski, Dawid E. Krasoń, Piotr Number Theory 11G09, 14G32, 18G35 We introduce and study a natural class of Anderson t- modules, called triangular t-modules, characterized by having Drinfeld modules as their $τ$-composition factors. They form a homologically meaningful generalization of Drinfeld modules and exhibit rich arithmetic structure.\smallskip We establish criteria for purity, strict and almost strict, and develop a reduction procedure that lowers the degrees of the defining biderivations. As a consequence, every almost strictly pure triangular t-module becomes strictly pure after a finite base extension. We then investigate morphisms and isogenies between triangular t-modules, provide a characterization of triangular isogenies, and describe the algebra of endomorphisms, including a criterion for commutativity. On the analytic side, we show that all triangular t- modules are uniformizable and establish finiteness and purity criteria with consequences for Taelman's conjecture. Finally, we develop a duality theory for triangular t- modules and their biderivations, proving compatibility with $τ$-composition series and establishing analogues of the Cartier-Nishi theorem and the Weil-Barsotti formula. |
| title | Homological Methods in the Generalization of Drinfeld Modules |
| topic | Number Theory 11G09, 14G32, 18G35 |
| url | https://arxiv.org/abs/2512.07607 |