Taming wild extensions with Hopf algebras
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- by Lindsay N. Childs PDF
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Abstract:
Let $K \subset L$ be a Galois extension of number fields with abelian Galois group $G$ and rings of integers $R \subset S$, and let $\mathcal {A}$ be the order of $S$ in $KG$. If $\mathcal {A}$ is a Hopf $R$-algebra with operations induced from $KG$, then $S$ is locally isomorphic to $\mathcal {A}$ as $\mathcal {A}$-module. Criteria are found for $\mathcal {A}$ to be a Hopf algebra when $K = {\mathbf {Q}}$ or when $L/K$ is a Kummer extension of prime degree. In the latter case we also obtain a complete classification of orders over $R$ in $L$ which are tame or Galois $H$-extensions, $H$ a Hopf order in $KG$, using a generalization of the discriminant.References
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Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 304 (1987), 111-140
- MSC: Primary 11R33; Secondary 16A24
- DOI: https://doi.org/10.1090/S0002-9947-1987-0906809-8
- MathSciNet review: 906809