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<p>We show that for any separably closed field <i>k</i> of characteristic <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(p&gt;0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>, the canonical functor from nilpotent <i>p</i>-adic spaces to <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\mathbb {E}_\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">E</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation>-coalgebras over <i>k</i> (given by singular chains with coefficients in <i>k</i>) is fully faithful. We also identify the essential image of simply connected spaces inside coalgebras. This dualizes and removes finiteness assumptions from a theorem of Mandell.</p>

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\(\mathbb {E}_\infty \)-coalgebras and p-adic homotopy theory

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月23日

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  • Tom Bachmann,
  • Robert Burklund

摘要

We show that for any separably closed field k of characteristic \(p>0\) p > 0 , the canonical functor from nilpotent p-adic spaces to \(\mathbb {E}_\infty \) E ∞ -coalgebras over k (given by singular chains with coefficients in k) is fully faithful. We also identify the essential image of simply connected spaces inside coalgebras. This dualizes and removes finiteness assumptions from a theorem of Mandell.