<p>The dual motivic Steenrod algebra with mod <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\ell \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ℓ</mi> </math></EquationSource> </InlineEquation> coefficients was computed by Voevodsky over a base field of characteristic zero, and by Hoyois, Kelly, and Østvær over a base field of characteristic <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(p \ne \ell \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>≠</mo> <mi>ℓ</mi> </mrow> </math></EquationSource> </InlineEquation>. In the case <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(p = \ell \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>=</mo> <mi>ℓ</mi> </mrow> </math></EquationSource> </InlineEquation>, we show that the conjectured answer is a retract of the actual answer. We also describe the slices of the algebraic cobordism spectrum <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\textrm{MGL}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>MGL</mtext> </math></EquationSource> </InlineEquation>: we show that the conjectured form of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(s_n \textrm{MGL}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>s</mi> <mi>n</mi> </msub> <mtext>MGL</mtext> </mrow> </math></EquationSource> </InlineEquation> is a retract of the actual answer.</p>

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Towards the dual motivic Steenrod algebra in positive characteristic

  • Martin Frankland,
  • Markus Spitzweck

摘要

The dual motivic Steenrod algebra with mod \(\ell \) coefficients was computed by Voevodsky over a base field of characteristic zero, and by Hoyois, Kelly, and Østvær over a base field of characteristic \(p \ne \ell \) p . In the case \(p = \ell \) p = , we show that the conjectured answer is a retract of the actual answer. We also describe the slices of the algebraic cobordism spectrum \(\textrm{MGL}\) MGL : we show that the conjectured form of \(s_n \textrm{MGL}\) s n MGL is a retract of the actual answer.