2025/12/08 by Kędzierski, Dawid E., Krasoń, Piotr
Mathematics · #11G09 #14G32 #18G35 #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Rings, Modules, and Algebras
paper · doi:10.48550/arxiv.2512.07607
openalex publication_date 2025/12/08 · openalex created_date 2025/12/10 · openalex updated_date 2026/07/28
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.