# 谱序列的五项正合列　`prop.five-term-spectral-sequence`
命题：$0 \to E^{1,0}_{2} \to H^{1} \to E^{0,1}_{2} \xrightarrow{d_{2}} E^{2,0}_{2} \to H^{2}$
layer 18 · 命题 · 过滤与谱序列 · 同调代数
[在星图里打开](../#n=prop.five-term-spectral-sequence)　·　[节点索引](../index.md)

第一象限谱序列 $E^{p,q}_{2} \implies H^{p+q}$ 给出**五项正合列**
> 陈述续见 [nodes/prop.five-term-spectral-sequence.2.md](./prop.five-term-spectral-sequence.2.md)


## 它能推出什么 / 谁在用它
- ⇒ [`prop.cech-h1-equals-h1`](../nodes/prop.cech-h1-equals-h1.md) 一次 Čech 就是一次上同调

## 为什么成立（入边，证明在 proofs/）
- …另有入边，续页见 [nodes/prop.five-term-spectral-sequence.3.md](./prop.five-term-spectral-sequence.3.md)

refs: Le Stum, An introduction to condensed mathematics, Exercise 7.30

> 说明见 `notes/prop.five-term-spectral-sequence.md`

引用：`prop.five-term-spectral-sequence`（内容 v0.9.0）· 条款见 [LICENSE.txt](../LICENSE.txt)