等变上同调与ech超上同调的同构定理

An Isomorphism Theorem Between Equivariant Cohomology and ech Hypercohomology

首先证明了任意一个等变微分流形都存在等变良好开覆盖,且等变良好开覆盖集所组成的集合在全部开覆盖组成的集合中共尾.在此基础上,证明了等变上同调与ech超上同调的同构.此定理可应用于实代数簇的Deligne上同调研究.

We first show that each equivariant smooth manifold has an equivariant good cover, and the equivariant good covers are cofinal in the set of open covers. We further this result to get an isomorphism theorem between equivariant cohomology and Cech hypercohomology. Such result can be applied to the study of Deligne cohomology of the real algebraic varieties.