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- The first of these is the development of an axiomatic treatment of sheaf theory by Grothendieck for the purpose of to define sheaf cohomology. 但是，数学的逻辑推导之前，总需要有一些基本的定义与公理。
- These two theorems will be derived later from results on nonabelian cohomology. 这两个定理将在后面由非交换上同调的结果推出。
- The author proved that there is an abelian group homomorphism between the Grothendieck groups of ?R? and ?A?. 作者证明了在R的Grothendieck群和A的Grothendieck群之间存在一个阿贝尔群同态.
- Later Chen and Hu[CH] give adeRham model to compute the Chen-Ruan cohomology ring of abelian orbifold. 最近;B.;Chen 和S
- Many properties of twisted conjugate actions can be expressed by the language of nonabelian cohomology, and vise versa. 扭共轭作用的很多性质可以用非交换上同调的语言来表述，反之亦然。
- For applications to homotopy theory we also discuss by way of analogy cohomology with arbitrary coefficients. 蔡皋把想象的虚无缥缈的乌托邦具象化。让人感觉到一个实实在在的桃花源。
- But twisted conjugate actions of Lie groups have closed relation with nonabelian cohomology of cyclic groups with coefficients in Lie groups. 而李群的扭共轭作用与循环群以李群为系数的非交换上同调有非常密切的关系。
- Chen and Ruan[CR1] defined a very interesting cohomology theory for orb-ifold, which is now called Chen-Ruan cohomology. Chen 和Y.;Ruan[CR1] 对orbifold 定义了一种非常有意义的上同调理论;现在称为Chen-Ruan 上同调
- Further, we've generalized the famous Liouville's theorem in classical mechanics and linked the Noether theorem with the cohomology. 提出相空间上保体积的一般方程，通常的正则方程是其特殊形式；
- In some finiteness conditions, we prove that there exists a natural Abelian group homomorphism from the Grothendieck group of R to the Grothendieck group of A. 在适当的有限性条件下，我们证明了一个从R的Grothendieck群到A的Orothendieck群的自然的阿贝尔群同态。
- For a general twisted conjugate action, the orbit space can be expressed as the nonabelian cohomology of the infinite cyclic group. 对于一般的扭共轭作用，其轨道空间可以表示为无限循环群的非交换上同调。
- If moreover the automorphism involved is of finite order, some special orbits are related to the nonabelian cohomology of a finite cyclic group. 当扭共轭作用中的自同构为有限阶时，某些特殊的轨道对应于有限循环群的非交换上同调。
- Some acquaintance with manifolds, simplicial complexes, singular homology and cohomology, and homotopy groups is helpful, but not really necessary. 再比如渔人从桃花源出来的时候，桃花源的人送给他一包礼物里面有种子和一只拨浪鼓。
- Moreover, some results on nonabelian cohomology of finite cyclic groups with coefficients in Lie groups can be also generalized to the case of finite non-cyclic groups. 而有限循环群李群系数非交换上同调的一些结果，还可以推广到有限非循环群的情况。
- We study the properties of filter-regular sequences, and obtain the equivalence characterizations on balanced big filter-modules in terms of cousin complex and local cohomology theory. 通过对 filter-正则元及 filter-正则序列的研究 ;利用 Cousin复形 ;局部上同调等一些用于研究banlanced big Cohen-Macaulay模的工具及思想方法 ;给出了关于 balanced big filter-模的一些等价刻划 .
- In the paper, we consider 2-cocycles on an infinite-dimensional Lie algebra L. We obtain all of the 2-cocycles on this Lie algebra and further determine its second cohomology group. 摘要考虑了一类无限维李代数L的二上圈。通过计算，得到了此类李代数的所有的二上圈，从而确定了L的二上同调群。
- It is expected that those algebraic methods also apply to questions on nonabelian cohomology with coefficients in Lie groups, and then we can get information of twisted conjugate actions. 可以预期，这些代数方法也可以用来研究李群系数的非交换上同调的性质，从而得到李群扭共轭作用的性质。
- The Algebra of Secondary Cohomology Operations 二阶上同调运算代数
- Cohomology Elements of Character Triples 特征标三元组的上同调元素
- cup product of the cohomology group 上同调群的的上积
