The adjoint of the Carlitz module and Fermat's Last Theorem
type: Item
instance of: scholarly article
title: The adjoint of the Carlitz module and Fermat's Last Theorem
zbMATH Open document ID: 0906.11030
published in: Finite Fields and their Applications
publication date: 1999-02-16T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 11G09
Mathematics Subject Classification ID: 11D41
zbMATH DE Number: 759425
zbMATH Keywords: adjoints of additive polynomials
zbMATH Keywords: adjoint Drinfeld modules
zbMATH Keywords: Fermat's equation for function fields
zbMATH Keywords: Carlitz module
author: David Goss
reviewed by: Marc Reversat
MaRDI profile type: Publication
full work available at URL: ffta.1995.1014
OpenAlex ID: W1987827022
DOI: 10.1006/FFTA.1995.1014
description: scientific article; zbMATH DE number 759425