Module of Kahler differentials for manifolds
Let $ A$ be a $ k$ -algebra and let $ \mathcal{M}_A$ be the set of all $ A$ -modules. In $ \mathcal{M}_A$ , there exists a universal object $ \Omega_{A/k}$ , called the module of Kahler differentials,...
View ArticleDifferentials in Weil model for equivariant cohomology
Why should we define the differential in Weil model as follows? I could understand $ \sum_{j,k} c_{jk}^i \theta_j \wedge \theta_k$ plays a role in the formula because it is the dual of the structure...
View ArticleDifferentials as basis vectors for one form
For i$ \in [1,n]$ let $ dx_i$ be a function that assigns to $ v\in \mathbb{R}^n$ its ith component. Then $ dx_i(v)=v_i$ is a 1-form. Proof: 1) $ dx_i(v+w)=(v+w)_i =v_i+w_i$ (by definition of vector...
View ArticleNotational question about quadratic differentials in Strebel’s book...
In Kurt Strebel’s book “Quadratic Differentials”, in Chapter 2, $ \S4$ , he begins by saying: “Every analytic function $ \varphi$ is a domain $ G$ of the $ z$ -plane defines, in a natural way, a field...
View ArticleComputing the differentials in the Adams spectral sequence
Assume you are given an explicit presentation of the $ E_2$ -terms of the Adams spectral sequence. Are the differentials on $ E_2$ and further algorithmically computable? I do not care how practical...
View ArticleSheaf of Kähler Differentials is Invertible in Dense Open Subset
Let $ f:S→B$ be an elliptic fibration from an integral surface $ S$ to integral curve $ B$ . Here I use following definitions: A surface (resp. curve) is a $ 2$ -dim (resp. $ 1$ -dim) proper k scheme...
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