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<p>Let <i>p</i> be an odd prime number. For a degree <i>p</i> extension of <i>p</i>-adic fields <i>L</i>/<i>K</i>, we give a complete characterization of the condition for the ring of integers <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {O}_L\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">O</mi> <mi>L</mi> </msub> </math></EquationSource> </InlineEquation> to be free as a module over its associated order in the unique Hopf-Galois structure on <i>L</i>/<i>K</i>.</p>

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Hopf-Galois module structure of degree p extensions of p-adic fields

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  • 发表日期：

    2026年7月9日

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  • Daniel Gil-Muñoz

摘要

Let p be an odd prime number. For a degree p extension of p-adic fields L/K, we give a complete characterization of the condition for the ring of integers \(\mathcal {O}_L\) O L to be free as a module over its associated order in the unique Hopf-Galois structure on L/K.