论文标题
atiyah-bott在doivariant witt coomomology中的本地化
Atiyah-Bott localization in equivariant Witt cohomology
论文作者
论文摘要
令$ n $为对角圆环的标准器$ t_1 \ cong \ mathbb {g} _m $ in $ \ text {sl} _2 $。我们证明了$ \ text {sl} _2^n $和$ n^n $的本地化定理，用于等效的共同体，以及（扭曲的）witt sheaf中的系数，沿古典atiyah-bott bott局部定位定理，用于托鲁斯动作的等效共同体。我们也有一个类似于$ \ text {sl} _2^n $和$ n $的Bott残留公式的类似物。如果是$ \ text {sl} _2^n $ action，则对轨道类型有相当严重的限制。对于$ n $ -ACTION，本地化结果没有限制，但是对于Bott残留定理，需要对$ T_1 $ -ACTION的固定点进行一定类型的分解。
Let $N$ be a normalizer of the diagonal torus $T_1\cong \mathbb{G}_m$ in $\text{SL}_2$. We prove localization theorems for $\text{SL}_2^n$ and $N^n$ for equivariant cohomology with coefficients in the (twisted) Witt sheaf, along the lines of the classical Atiyah-Bott localization theorems for equivariant cohomology for a torus action. We also have an analog of the Bott residue formula for $\text{SL}_2^n$ and $N$. In the case of an $\text{SL}_2^n$-action, there is a rather serious restriction on the orbit type. For an $N$-action, there is no restriction for the localization result, but for the Bott residue theorem, one requires a certain type of decomposition of the fixed points for the $T_1$-action.
