Breuil-Kisin modules and Hopf orders in cyclic group rings

2010/01/12 by Alan Koch, Koch, Alan
Mathematics · #14L15 #16T05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:14L15 #msc:16T05

paper · pdf · doi:10.48550/arxiv.1001.1929

17 pages

arxiv created 2010/01/14 · arxiv updated 2010/02/26

Abstract

For K an extension of 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 p². We also give a Laurent series interpretation of the Breuil-Kisin modules that give these Hopf orders.

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