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<p>We examine the ramification groups of finite Galois extensions over complete discrete valuation fields of equal characteristic <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(p&gt;0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>. Brylinski (1983) calculated the ramification groups in the case where the Galois groups are abelian. We extend the results of Brylinski to some non-abelian cases where the Galois groups are of order <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\le p^{p+1}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>≤</mo> <msup> <mi>p</mi> <mrow> <mi>p</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> and of maximal nilpotency class.</p>

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Ramification groups of some finite Galois extensions of maximal nilpotency class over local fields of positive characteristic

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  • 发表日期：

    2025年8月28日

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  • Koto Imai

摘要

We examine the ramification groups of finite Galois extensions over complete discrete valuation fields of equal characteristic \(p>0\) p > 0 . Brylinski (1983) calculated the ramification groups in the case where the Galois groups are abelian. We extend the results of Brylinski to some non-abelian cases where the Galois groups are of order \(\le p^{p+1}\) ≤ p p + 1 and of maximal nilpotency class.