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Results tagged with ac.commutative-algebra
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user 2653
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
14
votes
Accepted
An example where GCD depends on the domain
(Edit: first version was about lcm rather than gcd).
Take $R=k[u,v,w]$, $a=uv$, $b=vw$. Then $gcd_R(a,b)=v$ (times constant). Now let $S=k[a,b]$. Since $a$ and $b$ are independent, $gcd_S(a,b)=1$ (tim …
- 4,540
10
votes
Accepted
When does a quasicoherent sheaf vanish?
If the scheme is locally noetherian, this is true and can be proved by noetherian induction. In fact, you can even replace $M$ with an object of bounded derived quasi-coherent category, if you are int …
- 4,540
3
votes
Accepted
'Strong' density of differential operators in linear operators
I think it may be easier if you do not choose the open cover in advance, so that the cover may depend on $M$. Equivalently, let us work with local rings first.
Here is a sketch of the argument. I am …
- 4,540
14
votes
Accepted
Derivations of C(X)? or Why Must Supermanifolds be Smooth?
Here's a proof from definition. (I don't think it has anything to do with compactness.) Let us show that derivation
$\delta:C(X)\to C(X)$ vanishes for any topological manifold $X$. Indeed, $\delta(1) …
- 4,540