# Tagged Questions

**2**

votes

**1**answer

270 views

### Frobenius base change of etale maps

Let $A$ be a characteristic $p>0$ commutative ring. Let $B$ be a finitely presented etale $A$ algebra i.e.
$$
B=A[x_1,\ldots,x_n]/(f_1,\ldots,f_n),
$$
with $det(\frac{\partial f_i}{\partial ...

**1**

vote

**0**answers

328 views

### elementary exact sequence of normal sheaves

Let $Z \subset Y \subset \mathbb{A^n}$ be a smooth subvarieties of $\mathbb{A^n}$.
I'm trying to show that there is an exact sequence of normal bundles.
$0 \rightarrow N_{Z/Y} \rightarrow N_{Z} ...

**4**

votes

**1**answer

423 views

### Localizability of differential operators a la Grothendieck

Hello,
Maybe this question is trivial, so sorry
Let $A$ be a (comm. with 1) $k$-algebra, where $k$ is a ring (comm. with 1).
Then we can define the module of differential operators $D^{\leq n} ...

**1**

vote

**1**answer

270 views

### Presentation of finite modules with null annihilator

Let $R$ be a noetherian local ring and let $M$ be a finite $R$-module. Assume that the annihilator of $M$ is zero. Consider a minimal presentation of M as follows: ...

**2**

votes

**2**answers

307 views

### vectors with entries from a finite ring

I've been working recently with vectors over finite fields, but I was hoping to work in a more general setting and consider vectors over finite commutative rings. The question I had is as follows: if ...

**12**

votes

**4**answers

4k views

### Atiyah-MacDonald, exercise 2.11

Let A be a commutative ring with 1 not equal to 0. (The ring A is not necessarily a domain, and is not necessarily noetherian.) Assume we have an injective map of free A-modules A^m -> A^n. Must we ...