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Carlitz Modules and Galois Module Structure

✍ Scribed by Akira Aiba


Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
609 KB
Volume
62
Category
Article
ISSN
0022-314X

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✦ Synopsis


Let k be a one variable rational function field over a finite field. We construct an example of a wildly ramified abelian extension over k, whose integer ring is not free over its associated order.


πŸ“œ SIMILAR VOLUMES


Carlitz Modules and Galois Module Struct
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Let L#F be cyclotomic function fields of Carlitz. We show that if LΓ‚F is Carlitz Kummer, the integer ring O L is free over the associated order as in the classical cyclotomic Kummer extension. However, contrary to the characteristic zero case, O L is not free unless LΓ‚F is Carlitz Kummer.

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Let \(K\) be a quadratic imaginary number field and \(R_{f}\) the ring class field modulo \(f\) over \(K, f \in \mathbb{N}\). Let \(\theta_{f}\) denote the order of conductor \(f\) in \(K\) and let \(\mathfrak{g}^{*}, \mathrm{~g}\) be proper O \(\gamma\)-ideals such that \(\mathbf{g}^{* 2} \subseteq

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