论文标题
高级霍希柴尔德共同研究方案
Higher order Hochschild cohomology of schemes
论文作者
论文摘要
我们表明，与连接的尖头简单集合相关的较高的Hochschild络合物与特征零字段上的通勤代数的定位相关联。然后，我们以两种方式定义了在特征零领域的方案的高级Hochschild协同学。最初，我们可以采用与较高的Hochschild Presheaf相关的Shyprext函数。我们在特征零领域的平滑代数品种的高阶Hochschild共同体中获得了hodge分解，该杂种构成了Pirashvili的Hodge分解。我们还可以通过将其结构前exeaf的ext函数取在较高的Hochschild Presheaf的d -1的较高的hochschild Presheaf上，来定义分离方案D顺序的较高的Hochschild阶段。我们还将天鹅定义的等效性概括为在一个领域上的任何分离方案。
We show that Higher Hochschild complex associated to a connected pointed simplicial set commutes with localization of commutative algebras over a field of characteristic zero. Then, we define in two ways higher order Hochschild cohomology of schemes over a field of characteristic zero. Originally, we can take the hyperext functor of the sheaf associated to Higher Hochschild presheaf. We obtain a Hodge decomposition for higher order Hochschild cohomology of smooth algebraic varieties over a field of characteristic zero which generalizes Pirashvili's Hodge decomposition. We can also define the Higher Hochschild cohomology of order d of a separated scheme by taking the ext functor of its structure presheaf over the Higher Hochschild presheaf of order d -- 1. These two definitions are really close to those of Swanfor classical Hochschild cohomology, but our tools are model categories and derived functors. We also generalize the equivalence of Swan's definitions to any separated schemes over a field.
