摘要翻译：
设X是具有代数群G作用的代数簇。假设X有一个完全例外的束集，并且这些束集在群的作用下是不变的。我们构造了X上G-等变相干束的有界导范畴的半守恒分解，它等价于群的扭曲表示的导范畴。如果群在零特征的代数闭域上是有限的或约化的，这就给出了导出的等变范畴中的一个完全例外集合。我们将我们的结果应用于特定的变体，如射影空间、二次曲面、Grassmanians曲面和Del Pezzo曲面。
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英文标题：
《Semiorthogonal decompositions of derived categories of equivariant
  coherent sheaves》
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作者：
Alexei Elagin
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最新提交年份：
2008
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分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
  Let X be an algebraic variety with an action of an algebraic group G. Suppose X has a full exceptional collection of sheaves, and these sheaves are invariant under the action of the group. We construct a semiorthogonal decomposition of bounded derived category of G-equivariant coherent sheaves on X into components, equivalent to derived categories of twisted representations of the group. If the group is finite or reductive over the algebraically closed field of zero characteristic, this gives a full exceptional collection in the derived equivariant category. We apply our results to particular varieties such as projective spaces, quadrics, Grassmanians and Del Pezzo surfaces.
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PDF链接：
https://arxiv.org/pdf/0809.5166