Fitting ideals of Class groups in Carlitz-Hayes cyclotomic extensions

2018/11/15 by Bandini, Andrea, Bars, Francesc, Coscelli, Edoardo
#11M38 #11R23 #11R58 #11R60 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1811.06611

Abstract

We generalize some results of Greither and Popescu to a geometric Galois cover X→ Y which appears naturally for example in extensions generated by \mathfrakpⁿ-torsion points of a rank 1 normalized Drinfeld module (i.e. in subextensions of Carlitz-Hayes cyclotomic extensions of global fields of positive characteristic). We obtain a description of the Fitting ideal of class groups (or of their dual) via a formula involving Stickelberger elements and providing a link (similar to the one in \citeABBL) with Goss ζ-function.

Related

• Iwasawa Main Conjecture for the Carlitz cyclotomic extension and applications
• Galois action on class groups
• Ideal class groups of cyclotomic number fields II
• Aspects of Iwasawa theory over function fields
• The Spiegelungssatz for the Carlitz module