# Tagged Questions

**6**

votes

**0**answers

166 views

### The Rappoport-Zink spectral sequence vs. the one of the complement of a normal crossing divisor

As far as I understand these matters, for a regular $\mathfrak{X}$ that is proper flat of finite type over $\operatorname{Spec}\mathbb{Z}_p$, the Rappoport-Zink spectral sequence relates the etale ...

**5**

votes

**1**answer

330 views

### Vanishing cycles of a locally constant sheaf for a smooth morphism in the $l = p$-case

$\DeclareMathOperator{\Spec}{Spec}$
My question is concerned with vanishing cycles of a locally constant sheaf for a smooth morphism in the case $l = p$. In the case $l \neq p$ this is a statement in ...

**15**

votes

**3**answers

2k views

### Vanishing cycles in a nutshell?

To quote one source among many, "the general reference for vanishing cycles is [SGA 7] XIII and XV". Is there a more direct way to learn the main principles of this theory (i.e. without the language ...

**28**

votes

**4**answers

3k views

### Is there a good way to think of vanishing cycles and nearby cycles?

Once in a while I run into literature that invokes vanishing cycle machinery with a cryptic sentence like, "this follows from a standard vanishing cycle argument." Is there a good way to look at ...

**5**

votes

**2**answers

687 views

### Higher vanishing cycles

The generalisation of the vanishing cycle formalism in SGA 7 is apparently since the 1970's an issue, Morava mentioned a connection with Bousfield localization. I find the Morava's remarks ...