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<p>We show that for a large class of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>∞</mi> </math></EquationSource> </InlineEquation>-topoi there exist unstable arithmetic fracture squares, i.e. squares which recover a nilpotent sheaf <i>F</i>as the pullback of the rationalization of <i>F</i> with the product of the <i>p</i>-completions of <i>F</i> ranging over all primes <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(p\in {\mathbb {Z}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>∈</mo> <mi mathvariant="double-struck">Z</mi> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Unstable arithmetic fracture squares in \(\infty \)-topoi

  • 期刊论文

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  • 发表日期：

    2026年1月23日

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  • Klaus Mattis

摘要

We show that for a large class of \(\infty \) ∞ -topoi there exist unstable arithmetic fracture squares, i.e. squares which recover a nilpotent sheaf Fas the pullback of the rationalization of F with the product of the p-completions of F ranging over all primes \(p\in {\mathbb {Z}}\) p ∈ Z .