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<p>Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(X=G/H\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>X</mi> <mo>=</mo> <mi>G</mi> <mo stretchy="false">/</mo> <mi>H</mi> </mrow> </math></EquationSource> </InlineEquation> be a homogeneous spherical variety over an algebraically closed field of characteristic <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(p\ge 0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>≥</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>. We compute the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(p'\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>p</mi> <mo>′</mo> </msup> </math></EquationSource> </InlineEquation>-parts of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\pi _0(H)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>π</mi> <mn>0</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>H</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\pi _1(X)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>π</mi> <mn>1</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> from the spherical system of <i>X</i>.</p>

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On the Fundamental Group of a Spherical Variety

  • 期刊论文

  • 发表日期：

    2025年3月20日

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  • Friedrich Knop

摘要

Let \(X=G/H\) X = G / H be a homogeneous spherical variety over an algebraically closed field of characteristic \(p\ge 0\) p ≥ 0 . We compute the \(p'\) p ′ -parts of \(\pi _0(H)\) π 0 ( H ) and \(\pi _1(X)\) π 1 ( X ) from the spherical system of X.