分权与派生德拉姆同调

Kirill Magidson
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引用次数: 0

摘要

我们发展了派生分权代数的形式主义,并在此框架内重温了派生德拉姆与晶体同调的理论。我们用衍生交换环 $A$ 的最大滤波除幂增厚这一普遍性质来描述衍生交换环 $A$ 的衍生 De Rham 同调及其上的霍奇滤波。我们证明了我们的方法与 A.Raksit 的方法一致。在此过程中,我们发展了派生代数几何中与派生德拉姆同调相关的平方零扩展和派生的一些基本原理。
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Divided Powers and Derived De Rham Cohomology
We develop the formalism of derived divided power algebras, and revisit the theory of derived De Rham and crystalline cohomology in this framework. We characterize derived De Rham cohomology of a derived commutative ring $A$, together with the Hodge filtration on it, in terms of a universal property as the largest filtered divided power thickening of $A$. We show that our approach agrees with A.Raksit's. Along the way, we develop some fundamentals of square-zero extensions and derivations in derived algebraic geometry in connection with derived De Rham cohomology.
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