上同调Hasse原理与商奇点的分解
Cohomological Hasse principle and resolution of quotient singularities
摘要：
本文研究奇异格式的权同调。权同调是奇异概型的一个不变量，它是由奇异点的奇点的分解的超覆盖定义的。我们的主要结果是商奇点的权同调的McKay原理，即我们用等变概型的权同调来描述商概型的权同调。我们的方法是减少几何McKay原则的重量同源加藤的上同调Hasse原则的算术计划。权同调的McKay原理隐含了商奇点分解的例外因子的对偶复形的同伦型McKay原理。因此，我们证明了对偶复形是可收缩的孤立商奇点。
英文摘要：
In this paper we study weight homology of singular schemes. Weight homology is an invariant of a singular scheme defined in terms of hypercoverings of resolution of singularities. Our main result is McKay principle for weight homology of quotient singularities, i.e. we describe weight homology of a quotient scheme in terms of weight homology of an equivariant scheme. Our method is to reduce the geometric McKay principle for weight homology to Kato's cohomological Hasse principle for arithmetic schemes. The McKay principle for weight homology implies McKay principle for the homotopy type of the dual complex of the exceptional divisors of a resolution of a quotient singularity. As a consequence we show that the dual complex is contractible for isolated quotient singularities.
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