论文标题
图形群体iMbeddings的衍生类别
Equivariant Derived Categories for Toroidal Group Imbeddings
论文作者
论文摘要
令$ \ text {x} $表示一个代数封闭的字段上的投影变化，线性代数组的作用有限许多轨道。 Then, a conjecture of Soergel and Lunts in the setting of Koszul duality and Langlands' philosophy, postulates that the equivariant derived category of bounded complexes with constructible equivariant cohomology sheaves on $\text{X}$ is equivalent to a full subcategory of the derived category of modules over a graded ring defined as a suitable graded $Ext$.到目前为止，仅证明了这种猜想的特殊情况。 {\本文的目的是为所有复杂的还原群的投射旋风嵌入提供证明。}实际上，我们表明，可以通过适当的修改来扩展Lunts用于证明的证明方法，以处理圆环Imbedding案例。 {\ IT，因为复杂还原群的每个模糊层都以环形嵌入为主导，因此我们的证明适用的品种类别很大。} 我们还表明，通常情况下，这种猜想是正确的障碍物，而当奇怪的尺寸高度相交的共同体学套管上消失时，这些猜想的一半消失了。在许多球形品种中，米歇尔·布里恩（Michel Brion）和作者在先前的工作中被证明了最后的消失条件是正确的。
Let $\text{X}$ denote a projective variety over an algebraically closed field on which a linear algebraic group acts with finitely many orbits. Then, a conjecture of Soergel and Lunts in the setting of Koszul duality and Langlands' philosophy, postulates that the equivariant derived category of bounded complexes with constructible equivariant cohomology sheaves on $\text{X}$ is equivalent to a full subcategory of the derived category of modules over a graded ring defined as a suitable graded $Ext$. Only special cases of this conjecture have been proven so far. {\it The purpose of this paper is to provide a proof of this conjecture for all projective toroidal imbeddings of complex reductive groups.} In fact, we show that the methods used by Lunts for a proof in the case of toric varieties can be extended with suitable modifications to handle the toroidal imbedding case. {\it Since every equivariant imbedding of a complex reductive group is dominated by a toroidal imbedding, the class of varieties for which our proof applies is quite large.} We also show that, in general, there exist a countable number of obstructions for this conjecture to be true and that half of these vanish when the odd dimensional equivariant intersection cohomology sheaves on the orbit closures vanish. This last vanishing condition had been proven to be true in many cases of spherical varieties by Michel Brion and the author in prior work.
