# Tagged Questions

**2**

votes

**0**answers

112 views

### scheme of sections over complete local ring

Let $f:X\rightarrow S= Spec(k[[\pi]])$ a finite type faithfully flat morphism.
Let $U\subset X$ be an open subset such that $U$ is smooth and surjective on $S$.
We consider the $k$-scheme ...

**1**

vote

**0**answers

101 views

### smooth morphism from a finite type source

Let $f: X\rightarrow Y$ a smooth morphism over a field $k$. We assume that $X$ is locally of finite type, does it imply that $Y$ is also locally of finite type?

**2**

votes

**0**answers

140 views

### fpqc, formal smoothness

Based on Possible formal smoothness mistake in EGA, let $X$ and $Y$ $k$-schemes ($k$ a field),
let $f:X\rightarrow Y$ a fpqc morphism such that $f$ is formally smooth and $X$ formally smooth, do we ...

**2**

votes

**0**answers

115 views

### descent for formally smooth maps

Let $f:X\rightarrow Y$ a morphism between schemes and $Y'\rightarrow Y$ a fpqc morphism
such that the base change $f'$ of $f$ to $Y'$ is formally smooth, does it imply that $f$ is formally smooth?

**13**

votes

**3**answers

837 views

### Is there an example of a variety over the complex numbers with no embedding into a smooth variety?

Is there an example of a variety over the complex numbers with no embedding into a smooth variety?

**10**

votes

**2**answers

1k views

### Is there an example of a formally smooth morphism which is not smooth?

A morphism of schemes is formally smooth and locally of finite presentation iff it is smooth.
What happens if we drop the finitely presented hypothesis? Of course, locally of finite presentation is ...

**6**

votes

**1**answer

389 views

### Can one check formal smoothness using only one-variable Artin rings?

Let f:X -> Y be a morphism of schemes over a field k. Can one check that f is formally smooth using only Artin rings of the form k'[t]/t^n, where k' is also a field?
Considering cuspidal curves one ...