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<p>In this work, we study Singer’s conjecture (Math Z 202:493–523, 1989) for the algebraic transfers of ranks 5 and 6 in the generic families of internal degrees. The Singer transfer serves as a valuable tool for understanding the structure of the cohomology of the Steenrod algebra, <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40574_2025_456_Article_IEq1.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="111" /> </InlineMediaObject> <EquationSource Format="TEX">\({\textrm{Ext}}_{{\mathscr {A}}}^{s}({\mathbb {F}}_2, \Sigma ^{k}{\mathbb {F}}_2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mtext>Ext</mtext> <mrow> <mi mathvariant="script">A</mi> </mrow> <mi>s</mi> </msubsup> <mrow> <mo stretchy="false">(</mo> <msub> <mi mathvariant="double-struck">F</mi> <mn>2</mn> </msub> <mo>,</mo> <msup> <mi mathvariant="normal">Σ</mi> <mi>k</mi> </msup> <msub> <mi mathvariant="double-struck">F</mi> <mn>2</mn> </msub> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>.</p>

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On an open conjecture for the algebraic transfer in generic families of internal degrees

  • 期刊论文

  • 发表日期：

    2025年1月28日

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  • Đặng Võ Phúc

摘要

In this work, we study Singer’s conjecture (Math Z 202:493–523, 1989) for the algebraic transfers of ranks 5 and 6 in the generic families of internal degrees. The Singer transfer serves as a valuable tool for understanding the structure of the cohomology of the Steenrod algebra, \({\textrm{Ext}}_{{\mathscr {A}}}^{s}({\mathbb {F}}_2, \Sigma ^{k}{\mathbb {F}}_2)\) Ext A s ( F 2 , Σ k F 2 ) .