# Tagged Questions

**7**

votes

**4**answers

798 views

### Coboundaries and Gluing in Cech Cohomology - Intuition?

I'm trying to develop an intuition for Cech cohomology geometrically, but am currently failing. A lot of people seem to say that the groups $H^n$ measure obstructions to gluing local sections to get ...

**13**

votes

**6**answers

832 views

### Understanding Adjointness of Sheaves in Algebraic Geometry

Pushforward and pullback are very basic operations in algebraic geometry, as is the adjointness between them. I worked out a very careful of adjointness of sheaves (below) when I was working out of ...

**7**

votes

**2**answers

487 views

### Interpreting $f^*f_*$

For a morphism of schemes $f: X\rightarrow Y$, one often considers the function $f^*f_*$ on sheaves. For example, this appears in adjunction for sheaves of $\mathcal{O}_X$-modules, the projection ...

**42**

votes

**5**answers

6k views

### What is sheaf cohomology intuitively?

What is sheaf cohomology intuitively?
For local systems it is ordinary cohomology with twisted coefficients. But what
if the sheaf in question is far from being constant?
Can one still understand ...

**16**

votes

**3**answers

2k views

### Stacks and sheaves

I'm a bit confused by the double role which sheaves play in the theory of stacks.
On the one hand, sheaves on a site are the obvious generalization of a sheaf on a topological space. On the other ...

**20**

votes

**4**answers

1k views

### Heuristic explanation of why we lose projectives in sheaves.

We know that presheaves of any category have enough projectives and that sheaves do not, why is this, and how does it effect our thinking?
This question was asked(and I found it very helpful) but I ...

**28**

votes

**4**answers

4k 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 ...