**0**

votes

**1**answer

67 views

### A confusion about covering flatness

I'm reading this entry on nLab. But I'm confusing with the notion of covering-flatness. More precisely, I meet some trouble when I try to show that the $Sets$-valued flatness is a special case of ...

**5**

votes

**0**answers

124 views

### Making the conceptual leap from locales to Grothendieck topologies?

I find the definition for locales and sheaves on locales to be straightforward, but I'm stumbling over the idea of a Grothendieck topology. Is there a nice way to see roughly how the latter ...

**2**

votes

**2**answers

272 views

### Morphism on schemes induced by continuous morphism of sites

I am beginner in the theory of Grothendieck topologies and I have the following question.
Let $X, Y$ be schemes over an algebraically closed field $k$. Denote by $X_{et}$ and $Y_{et}$ the Etale sites ...

**6**

votes

**1**answer

157 views

### Which dense inclusions of sites are ∞-dense?

An inclusion of sites f: D→C is dense if it induces an equivalence between the categories of sheaves on C and D.
Likewise, f is ∞-dense is it induces an equivalence between the ∞-categories of ...

**3**

votes

**2**answers

233 views

### 1st cech cohomology groups on ringed sites

Let $(C, O)$ be a ringed site -- i.e., $C$ is a small category with a grothendieck topology $\tau$ and $O$ a sheaf of rings on the site $(C,\tau)$. In this context, for any object $U$ of $C$ one can ...

**7**

votes

**1**answer

683 views

### Points in sites (etale, fppf, … )

I asked a part of this in an earlier question, but that part of my question didn't receive precedence.
Etale site is useful - examples of using the small fppf site?
Let $X$ be a scheme (assume it ...

**16**

votes

**1**answer

1k views

### Etale site is useful - examples of using the small fppf site?

Edit: After the answers and comments, I'm hoping for a little bit of elaboration (in the comment to the answer below.) Also, question 2 was discussed here:
Points in sites (etale, fppf, ... )
There, ...