论文标题
派生的抛物线诱导
Derived parabolic induction
论文作者
论文摘要
经典抛物线诱导函数是兰兰兹计划的代表理论方面的基本工具。在本文中，我们研究其派生版本。第二作者表明，超过$ k $，$ g $ a $ p $ a $ p $ addic还原群的派生类别和特征性$ p $的$ k $等同于某些分级分级$ k $ k $ k $ -algebra $ h__g h__g h_g h_g^\ bullet butter $的派出类别的类别，其零件是一种类别的组合，这是一个类别的keeroth hec，这是一个类别。这种等效性预测了我们在本文中构建的DG Hecke代数侧的衍生抛物线诱导函数的存在。这依赖于O. \Schnürer开发的差分等级类别的六函数形式主义理论。我们还讨论了衍生抛物线诱导的伴随函数。
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 $G$-representations over $k$, $G$ a $p$-adic reductive group and $k$ a field of characteristic $p$, is equivalent to the derived category of a certain differential graded $k$-algebra $H_G^\bullet$, 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.
