Iwasawa main conjecture for the Carlitz cyclotomic extension and applications

Bruno Anglès, Andrea Bandini, Francesc Bars, Ignazio Longhi

Research output: Contribution to journalArticleResearch


We prove an Iwasawa Main Conjecture for the class group of the p-cyclotomic extension F of the function field Fq(θ) (p is a prime of Fq[θ]), showing that its Fitting ideal is generated by a Stickelberger element. We use this and a link between the Stickelberger element and a p-adic L-function to prove a close analog of the Ferrero–Washington Theorem for F and to provide information on the p-adic valuations of the Bernoulli-Goss numbers β(j) (i.e., on the values of the Carlitz-Goss ζ-function at negative integers).
Original languageEnglish
Pages (from-to)1-36
JournalMathematische Annalen
Publication statusPublished - 1 Jan 2019


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