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9
votes
0answers
610 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
263 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
277 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
67 views

How to define Product of Conditional Measures?

I have been wondering how to define the product of conditional measures as defined by Renyi-Popper. I spell the details below. If $(X,\Sigma)$ is a measurable space, then the function $\mu : ...
3
votes
0answers
76 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
90 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
100 views

Definition of Givental $J$-function of cotangent bundle of flag variety

I would like to know the definition of Givental $J$-function of cotangent bundle of flag variety. To state my question more precisely, let us briefly recall the definition of the Givental $J$-function ...
2
votes
0answers
144 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
241 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
239 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
67 views

A certain Acyclic Partition of a digraph

Has the following object been defined in the literature? What is it called? And what literature studies it? Are there other characterizations of this? What properties are known? Let $G$ be a directed ...
0
votes
0answers
110 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 ...