Stickelberger series and Iwasawa Main Conjecture for Z∞pZp∞ -extensions of function fields
Let F:=Fq(θ)F:=Fq(θ) and let pp be a prime of A:=Fq[θ]A:=Fq[θ] (q=prq=pr and pp a prime). Let Fp/FFp/F be the pp -cyclotomic Z∞pZp∞ -extension of FF generated by the p∞p∞ -torsion of the Carlitz module and let ΛΛ be the associated Iwasawa algebra. We give an overview of the Iwasawa theory for the ΛΛ -module of divisor class groups and then define a Stickelberger series in Λ[[u]]Λ[[u]] , whose specializations enable us to prove an Iwasawa Main Conjecture for this setting. As an application we obtain a close analogue of the Ferrero-Washington theorem for FpFp . (Joint work with Bruno Anglès, Francesc Bars and Ignazio Longhi)