发表机构
Mathematical Institute, Tohoku University（东北大学数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明了连通复形对称代数的Koszul对偶，并构造了任意有限型分离概形的导出环路空间与切复形对称代数之间的导出范畴等价，推广了Kapranov的光滑情形结果。
AI 中文摘要
在本文中，我们证明了由有限秩局部自由层组成的连通复形的对称代数的Koszul对偶，该复形不必有下界。作为应用，我们构造了任意特征为零的域$k$上的有限型分离概形的导出环路空间的导出范畴与其切复形的对称代数之间的等价。这可被视为Kapranov在光滑情形下关于导出环路空间与余切丛的经典对偶的推广。我们还给出了我们的等价在导出形式叠方面的几何解释。
英文摘要
In this paper, we prove Koszul duality for symmetric algebras of connective complexes consisting of locally free sheaves of finite rank, which is not necessarily bounded below. As an application, we construct an equivalence between derived categories of derived loop spaces and the symmetric algebra of the tangent complex for arbitrary separated schemes of finite type over a field $k$ of characteristic zero. This can be regarded as a generalization of the classical duality between derived loop spaces and cotangent bundles by Kapranov in the smooth cases. We also give a geometrical interpretation of our equivalence in terms of derived formal stacks.
Comments28 pages
