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arXiv · 1001.1929

Breuil-Kisin modules and Hopf orders in cyclic group rings

Alan Koch
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Abstract

For $K$ an extension of $\mathbb{Q}_{p}$ with ring of integers $R$ we show how Breuil-Kisin modules can be used to determine Hopf orders in $K$-Hopf algebras of $p$-power dimension. We find all cyclic Breuil-Kisin modules, and use them to compute all of the Hopf orders in the group ring $KΓ$ where $Γ$ is cyclic of order $p$ or $p^{2}.$ We also give a Laurent series interpretation of the Breuil-Kisin modules that give these Hopf orders.

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Alan Koch. 2010-01-14. Breuil-Kisin modules and Hopf orders in cyclic group rings. https://arxiv.org/abs/1001.1929

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