Frobenius的Koszul对偶与半单性
Koszul duality and semisimplicity of Frobenius
摘要：
Beilinson-Ginzburg-Soergel的一个基本结果指出，在旗簇和相关空间上，l-adic反常层范畴的某个修改版本表现出一种称为Koszul对偶的现象。修改基本上包括丢弃的对象，其茎进行非半简单的行动弗罗贝纽斯。在本文中，我们证明了一些公共层函子（各种拉回和推进）诱导相应的函子修改范畴或其三角模拟。特别是，我们表明，这些函子保持半简单的Frobenius行动。
英文摘要：
A fundamental result of Beilinson-Ginzburg-Soergel states that on flag varieties and related spaces, a certain modified version of the category of l-adic perverse sheaves exhibits a phenomenon known as Koszul duality. The modification essentially consists of discarding objects whose stalks carry a nonsemisimple action of Frobenius. In this paper, we prove that a number of common sheaf functors (various pull-backs and push-forwards) induce corresponding functors on the modified category or its triangulated analogue. In particular, we show that these functors preserve semisimplicity of the Frobenius action.
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