dg-Hecke 对偶与张量积

Pub Date : 2024-07-16 DOI:10.1093/imrn/rnae156

Peter Schneider, Claus Sorensen

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引用次数: 0

摘要

我们继续[ 12]中开始的对单元范畴$D(G)$的研究。在同调层面上，我们把对偶函子 $R\underline{operatorname{Hom}}(-,k)$ 转移到了 dg 模块的派生范畴 $D(H_{U}^{\bullet})$。在这个过程中，我们开发了一种更通用、更精简的方法来处理[ 8] 中的反卷积 $\mathscr J$。我们还验证了 $D(G)$ 上的张量积对应于 dg 边上的操作张量积（参见 [ 5]）。这使用了施努勒关于具有模型结构的 dg 范畴的一个结果。

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dg-Hecke Duality and Tensor Products

We continue our study of the monoidal category $D(G)$ begun in [ 12]. At the level of cohomology we transfer the duality functor $R\underline{\operatorname{Hom}}(-,k)$ to the derived category of dg-modules $D(H_{U}^{\bullet })$. In the process we develop a more general and streamlined approach to the anti-involution $\mathscr J$ from [ 8]. We also verify that the tensor product on $D(G)$ corresponds to an operadic tensor product on the dg-side (cf [ 5]). This uses a result of Schnürer on dg-categories with a model structure.

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