Duality for t- modules: The Difficult Cases

Abstract

This paper continues our previous work on duality for Anderson $t$-modules. We study two dimensional triangular t-modules in a specific reduce form. Computer - assisted symbolic computations with matrices over a skew field revealed a reduction pattern for t-modules satisfying the ALD condition. Using this pattern, we prove that such t-modules are isomorphic to their double duals and extend the validity of the Cartier-Nishi theorem and the Weil-Barsotti formula to a substantially broader class of t-modules.