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arXiv · 1811.06611

Fitting ideals of Class groups in Carlitz-Hayes cyclotomic extensions

Andrea Bandini·Francesc Bars·Edoardo Coscelli
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Abstract

We generalize some results of Greither and Popescu to a geometric Galois cover $X\rightarrow Y$ which appears naturally for example in extensions generated by $\mathfrak{p}^n$-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 \cite{ABBL}) with Goss $ζ$-function.

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Andrea Bandini, Francesc Bars, Edoardo Coscelli. 2018-11-15. Fitting ideals of Class groups in Carlitz-Hayes cyclotomic extensions. https://arxiv.org/abs/1811.06611

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