# Čech 到上同调的谱序列　`cor.cech-cohomology-spectral`
推论：$\check{H}^{p}\bigl(X, H^{q}(M)\bigr) \Longrightarrow H^{p+q}(X, M)$
layer 19 · 推论 · 层上同调 · 同调代数
[在星图里打开](../#n=cor.cech-cohomology-spectral)　·　[节点索引](../index.md)

设 $\mathcal{C}$ 是有纤维积的 site、$X \in \mathcal{C}$、$M$ 是 $\mathcal{C}$ 上的**阿贝尔层**。则存在谱序列

$$E^{p,q}_{2} \;=\; \check{H}^{p}\bigl(X,\ H^{q}(M)\bigr) \;\Longrightarrow\; H^{p+q}(X,\ M),$$
> 陈述续见 [nodes/cor.cech-cohomology-spectral.2.md](./cor.cech-cohomology-spectral.2.md)


## 为什么成立（入边，证明在 proofs/）
- …另有入边，续页见 [nodes/cor.cech-cohomology-spectral.3.md](./cor.cech-cohomology-spectral.3.md)

## 它能推出什么 / 谁在用它
- …另有出边，续页见 [nodes/cor.cech-cohomology-spectral.4.md](./cor.cech-cohomology-spectral.4.md)

refs: Le Stum, An introduction to condensed mathematics, Corollary 7.3.8

> 说明见 `notes/cor.cech-cohomology-spectral.md`

引用：`cor.cech-cohomology-spectral`（内容 v0.9.0）· 条款见 [LICENSE.txt](../LICENSE.txt)