Given a smooth variety $X$ with an action of a finite group $G$, and a semiorthogonal decomposition of the derived category, $\mathcal{D}([X/G])$, of $G$-equivariant coherent sheaves on $X$ into subcategories equivalent to derived categories of smooth varieties, we construct a similar semiorthogonal decomposition for a smooth $G$-invariant divisor in $X$ (under certain technical assumptions). Combining this procedure with the semiorthogonal decompositions constructed in [18], we construct semiorthogonal decompositions of some equivariant derived categories of smooth projective hypersurfaces.

中文翻译：

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不变除数的等变派生类别的半正交分解

给定一个光滑的变量$ X $，它具有有限组$ G $的作用，并且对派生类别$ \ mathcal {D}（[X / G]）$，等于$ G $等变相干滑轮，进行半正交分解在将$ X $划分为与平滑变种的派生类别等效的子类别中，我们为$ X $中的平滑$ G $-不变除数构造了相似的半正交分解（在某些技术假设下）。将此程序与[18]中构造的半正交分解相结合，我们构造了光滑投影超曲面的某些等变派生类别的半正交分解。