Derived parabolic induction
Derived parabolic induction
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推导抛物线感应
DOI：
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发表时间：
2020
影响因子：
0.9
通讯作者：
P. Schneider
中科院分区：
文献类型：
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作者：
Sarah Scherotzke;P. Schneider
经典的抛物归纳函子是朗兰兹程序表示论方面的一个基本工具。在这篇文章中，我们研究它的衍生版本。第二作者证明了k$k$上的光滑G$G$-表示的导范畴，G$G$ a p$p$-adic约化群和k$k$ a特征p$p$域，等价于某个微分分次k$k$-代数HG·$H_G^的导范畴ullet$的第零上同调是一个经典的Hecke代数。这种等价性预言了在dg Hecke代数上存在一个导出的抛物诱导函子，我们在本文中构造了这个函子。这依赖于O.施纳勒我们还讨论了导出的抛物归纳法的伴随函子。
The classical parabolic induction functor is a fundamental tool on the representation theoretic side of the Langlands program. In this article, we study its derived version. It was shown by the second author that the derived category of smooth G$G$ ‐representations over k$k$ , G$G$ a p$p$ ‐adic reductive group and k$k$ a field of characteristic p$p$ , is equivalent to the derived category of a certain differential graded k$k$ ‐algebra HG•$H_G^ullet$ , whose zeroth cohomology is a classical Hecke algebra. This equivalence predicts the existence of a derived parabolic induction functor on the dg Hecke algebra side, which we construct in this paper. This relies on the theory of six‐functor formalisms for differential graded categories developed by O. Schnürer. We also discuss the adjoint functors of derived parabolic induction.