The adjoint of the Carlitz module and Fermat's Last Theorem
The author studies adjoints of additive polynomials and adjoint Drinfeld modules. He recalls the analog of Fermat's equation for function fields, involving the Carlitz module, introduced by \textit{D. Goss} [Math. Ann. 261, 269-286 (1982; Zbl 0494.12008)]. The analog of Fermat's Last Theorem has been proved by \textit{L. Denis} [Trans. Am. Math. Soc. 343, 713-726 (1994; Zbl 0811.11044)]. The author obtains FLT in function fields also, but for a ``Fermat's equation'' involving the adjoint of the Carlitz module. Section 5 contains open questions, and in an appendix (section 6) \textit{Yuichiro Taguchi} explains how the adjoints arise naturally in the context of \(\varphi\)-modules.
scientific article; zbMATH DE number 759425