Wojciech J. Gajda

Abstract: In this lecture we will introduce basic notions in function field theory, namely Drinfeld modules, Anderson t-modules, as well as the equivalent notions of t-motives and t-comotives. We will emphasize both the analogies and the significant differences between these objects and their counterparts in the mixed characteristic setting. After this brief introduction, I will describe results obtained in our recent work [3, 4, 5] concerning homological properties of the category of t-modules. Special attention will be devoted to duality theory. Our results in this direction generalize, on the one hand, the results of M. A. Papanikolas and N. Ramachandran [1], where a Weil–Barsotti formula for Drinfeld modules in the function field case, concerning Ext_1(E,C) (with E a Drinfeld module and C the Carlitz module), was proved, and on the other hand the results of Y. Taguchi [2].

Bibliography: [1] M. A. Papanikolas and N. Ramachandran, A Weil–Barsotti formula for Drinfeld modules, Journal of Number Theory 98 (2003), 407–431. [2] Y. Taguchi, A duality for finite t-modules, J. Math. Sci. Univ. Tokyo 2 (1995), 563–588. [3] D. E. Kedzierski and P. Krason, On Ext1 for Drinfeld modules, J. Number Theory 256 (2024), 97–135. [4] D. E. Kedzierski and P. Krason, Homological Methods in the Generalization of Drinfeld Modules, preprint, arXiv:2512.07607 (2025), 1–60. [5] D. E. Kedzierski and P. Krason, Weil–Barsotti formula for t-modules, J. Number Theory 278 (2026), 1–25.