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9
votes
0answers
604 views

What are the relationship between various definitions for quasi coherent sheaves?

It seems that there are many definitions of quasi coherent sheaves(modules). There is a nice page on nLab quasi coherent sheaves My questions are: Are there any other definitions of quasi coherent ...
5
votes
0answers
260 views

Why is Pic^0(C) of a curve C a variety?

Let $C$ be an abstract non-singular curve. I'm having a hard time finding a reference for why $\text{Pic}^0(C)$ is a variety. Any pointers towards a reference would be appreciated.
4
votes
0answers
271 views

Q-construction and Gabriel-Zisman Localization

It might be a stupid question. When I took a look at the definition of Q-construction. It makes for an exact category $P$, one defines a new category $QP$ whose objects are the same as $P$ but ...
3
votes
0answers
70 views

Non Borel Spaces: Gauge Integral

Question Is there a generalization of the gauge integral to measure spaces that do not necessarily arise out of some topology? I'm wondering since it seems as the gauge crucially uses ...
3
votes
0answers
87 views

On one class of Euclidean lattices

Let $\Lambda\subset \mathbb Z^3$ be 3D lattice with a basis $$a_1=\left(\begin{smallmatrix} a_{11} \\ a_{21}\\ a_{31} \end{smallmatrix}\right),a_2=\left(\begin{smallmatrix} a_{12} \\ a_{22}\\ a_{32} ...
2
votes
0answers
130 views

Alternate definition for the torsion tensor

I would be pleased to have some information about an alternate definition for the torsion tensor. Let us consider a smooth manifold $\mathcal{M}$ together with an arbitrary connection $\nabla$. The ...
2
votes
0answers
236 views

PAC field : Algebraically closed field :: ? : Henselian local ring

I'm wondering if the following exists in the world as a definition. I'll use the word "pseudo-Henselian." I'll restrict to DVRs for simplicity. I'd want to call a DVR $(R,\mathfrak{m})$ ...
2
votes
0answers
233 views

What is the analog of “monotonic” for scalar functions on surfaces?

"monotonic" is well defined for functions $f(x)$, where e.g. $x\in[0,1]$ and $f(x)\in\mathbb{R}$. The quality I particularly care about is that if $f(x)$ is monotonic then it will not have any local ...
0
votes
0answers
105 views

Name of Property $t=st \text{ and } s=ts$

What is the name of the property shared by a pair of functions $s,t$ with $$t=st \text{ and } s=ts$$ ( Main example: relation-valued domain and range operations on relations, via ...