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<p>Working at the prime 2 and chromatic height 2, we construct a finite resolution of the homotopy fixed points of Morava <i>E</i>-theory with respect to the subgroup <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="209_2025_3754_Article_IEq4.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {G}_2^1\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi mathvariant="double-struck">G</mi> <mn>2</mn> <mn>1</mn> </msubsup> </math></EquationSource> </InlineEquation> of the Morava stabilizer group. This is an upgrade of the finite resolution of the homotopy fixed points of <i>E</i>-theory with respect to the subgroup <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="209_2025_3754_Article_IEq5.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {S}_2^1\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi mathvariant="double-struck">S</mi> <mn>2</mn> <mn>1</mn> </msubsup> </math></EquationSource> </InlineEquation> constructed in work of Goerss–Henn–Mahowald–Rezk, Beaudry and Bobkova–Goerss.</p>

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The duality resolution at \(n=p=2\)

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月8日

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  • Agnès Beaudry,
  • Irina Bobkova,
  • Hans-Werner Henn

摘要

Working at the prime 2 and chromatic height 2, we construct a finite resolution of the homotopy fixed points of Morava E-theory with respect to the subgroup \(\mathbb {G}_2^1\) G 2 1 of the Morava stabilizer group. This is an upgrade of the finite resolution of the homotopy fixed points of E-theory with respect to the subgroup \(\mathbb {S}_2^1\) S 2 1 constructed in work of Goerss–Henn–Mahowald–Rezk, Beaudry and Bobkova–Goerss.