Illinois Journal of Mathematics

Duals of formal group Hopf orders in cyclic groups

Lindsay N. Childs and Robert G. Underwood

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Let $p$ be a prime number, $K$ be a finite extension of the $p$-adic rational numbers containing a primitive $p^n$th root of unity, $R$ be the valuation ring of $K$ and $G$ be the cyclic group of order $p^n$. We define triangular Hopf orders over $R$ in $KG$, and show that there exist triangular Hopf orders with $n(n+1)/2$ parameters by showing that the linear duals of "sufficiently $p$-adic" formal group Hopf orders are triangular.

Article information

Illinois J. Math., Volume 48, Number 3 (2004), 923-940.

First available in Project Euclid: 13 November 2009

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Zentralblatt MATH identifier

Primary: 16W30
Secondary: 11S31: Class field theory; $p$-adic formal groups [See also 14L05] 11S45: Algebras and orders, and their zeta functions [See also 11R52, 11R54, 16Hxx, 16Kxx] 14L05: Formal groups, $p$-divisible groups [See also 55N22]


Childs, Lindsay N.; Underwood, Robert G. Duals of formal group Hopf orders in cyclic groups. Illinois J. Math. 48 (2004), no. 3, 923--940. doi:10.1215/ijm/1258131060.

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