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<p>Let <i>G</i> be a connected reductive algebraic group with simply connected derived subgroup. Over the complex numbers there exists a local method to study the geometric properties of a point <i>g</i> in the closure of a Jordan class of <i>G</i> in terms of Jordan classes of a maximal rank reductive subgroup <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="31_2025_9931_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="59" /> </InlineMediaObject> <EquationSource Format="TEX">\(M \le G\)</EquationSource> </InlineEquation> depending on the point <i>g</i>, and further to the closures of certain decomposition classes in <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="31_2025_9931_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">\({\text {Lie}}M\)</EquationSource> </InlineEquation>. We adapt this method to the case of an algebraically closed field of characteristic <i>p</i>, and we give sufficient restrictions on <i>p</i> for it to hold.</p>

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Étale Geometry of Closures of Jordan Classes

  • 期刊论文

  • 发表日期：

    2025年9月12日

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  • Filippo Ambrosio

摘要

Let G be a connected reductive algebraic group with simply connected derived subgroup. Over the complex numbers there exists a local method to study the geometric properties of a point g in the closure of a Jordan class of G in terms of Jordan classes of a maximal rank reductive subgroup \(M \le G\) depending on the point g, and further to the closures of certain decomposition classes in \({\text {Lie}}M\) . We adapt this method to the case of an algebraically closed field of characteristic p, and we give sufficient restrictions on p for it to hold.