MathOverflow

I am interested in the Ziegler spectrum of $\mathcal{A}=Mod\text{-}kG$, the category of $kG$-modules, for $G$ a finite group and $k$ a field of characteristic $p$ dividing the order of the group. I suppose that the basic cases where $k=\mathbb{F}_p$...

$i=1,2,..,n$. $j=1,2,...,m$. Let $c_j>0$. Let $w_i>0$ and $\sum_{i} w_{i}=1$. Define $\alpha_j^i>0$ that $\sum_{j} \alpha_{j}^{i}=1$ for all $i$.
Define $a_{j}=\sum_{i} \alpha_{j}^{i} w_{i}$ and $r_{i \ell, j}=\frac{1}{2}\left(\alpha_{j}^{i}-\alpha_{j}^{\ell}\right)$....

Let $X_i$ ($i=1, \dots$) be an orthonormal basis for $L^2(\Omega, \mathbb P)$. In particular, it holds that $$\mathbb E[X_iX_j] = \delta_{ij}.$$Now take $Z\in L^2(\Omega, \mathbb P)$ and define $\tilde X_i:=ZX_i$. Let $\Sigma_m$ be the covariance matrix...

In GTM82, I read a model for the relative cohomology of (M,N) with N a submanifold of M.
And in the page: Relative De Rham cohomologies, I got to know that there is another model for relative cohomology by using differential forms of M, like those forms which restrict to 0 on N....