Orbifold Cohomology as Periodic Cyclic Homology
Orbifold Cohomology as Periodic Cyclic Homology
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作为周期循环同调的轨道上同调
DOI：
10.1142/s0129167x03001946
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发表时间：
2002
影响因子：
0.6
通讯作者：
V. Baranovsky
中科院分区：
文献类型：
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作者：
V. Baranovsky
从Feigin-Tsygan，Weibel和Keller的工作中可以知道，光滑复簇X的上同调群可以从（粗略地说）其导出的凝聚层范畴中恢复。本文证明了对于有限群G作用在X上，同样的程序应用于G-等变层，给出了X/G的轨道上同调。作为应用，在某些情况下，我们能够得到X/G的orbifold上同调和它的crepant分解的通常上同调之间的加性同构的简单证明（欧拉数和霍奇数的相等性在以前由不同的作者得到）。我们还陈述了一些关于产品结构的说明，以及奇异情况;以及与Kawamata最近的工作的联系。
It is known from the work of Feigin–Tsygan, Weibel and Keller that the cohomology groups of a smooth complex variety X can be recovered from (roughly speaking) its derived category of coherent sheaves. In this paper we show that for a finite group G acting on X the same procedure applied to G-equivariant sheaves gives the orbifold cohomology of X/G. As an application, in some cases we are able to obtain simple proofs of an additive isomorphism between the orbifold cohomology of X/G and the usual cohomology of its crepant resolution (the equality of Euler and Hodge numbers was obtained earlier by various authors). We also state some conjectures on the product structures, as well as the singular case; and a connection with a recent work by Kawamata.