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<p>We prove that, under a suitable condition on the contraction map of Hochschild homology, the shifted Hochschild cochain complex of a smooth proper stable <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>∞</mi> </math></EquationSource> </InlineEquation>-category is equivalent to an abelian dg Lie algebra. In particular, we show a generalization of Bogomolov–Tian–Todorov theorem to Calabi–Yau categories.</p>

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Bogomolov–Tian–Todorov theorem for Calabi–Yau categories

  • 期刊论文

  • 发表日期：

    2026年5月25日

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  • Isamu Iwanari

摘要

We prove that, under a suitable condition on the contraction map of Hochschild homology, the shifted Hochschild cochain complex of a smooth proper stable \(\infty \) ∞ -category is equivalent to an abelian dg Lie algebra. In particular, we show a generalization of Bogomolov–Tian–Todorov theorem to Calabi–Yau categories.