Recently Active Questions
159,066 questions
5
votes
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389
views
Is there a name for this differential operator and/or its corresponding spectrum?
Let $\mathcal{M}$ be a real, compact, orientable manifold and let $X$ be a vector field on $\mathcal{M}$. Consider the functional
$$E(f) = \int_{\mathcal{M}} X_p(f)^2 dV$$
where $X_p(f)$ is the ...
- 3,059
2
votes
2
answers
1k
views
What is it called if a vector space doesn't have an additive inverse?
so, you have, for any two members of the algebraic structure A and B and any nonnegative real values a, b:
two operations: * and +, such that
a*A + b*A = (a+b)*A is in the structure
A + B = B + A ...
- 2,284
2
votes
1
answer
244
views
Existence of smoothing of Calabi-Yau cones over $dP_{1}$ and $dP_{2}$
The blowdown of the zero section of the canonical bundle of the first del Pezzo surface $dP_{1}$, the blowup of $CP^{2}$ at one point, is a Calabi-Yau cone. I was just wondering if this cone admitted ...
- 28.9k
4
votes
2
answers
448
views
Can an abelian variety be represented as the cohomology of some other object?
Question
Given an abelian variety $V$ and an integer $n$, is there a natural abelian category with a natural object $X$ and natural coefficients $F$ so that $V\simeq H^n (X,F)$?
Motivation
Studying ...
- 436
0
votes
1
answer
118
views
Coaction on the Universal Calculus
Let $A$ be an algebra, $H$ a Hopf algebra, and
$$
\beta_A: A \to A \otimes H, ~~~~~ a \mapsto a^{(1)} \otimes a^{(2)}
$$
a right $H$-coaction. This induces a right $H$-coaction on $A \otimes A$ ...
- 47.3k
3
votes
2
answers
479
views
Extending maps of curves
(I'm happy to work over an algebraically closed field....)
Let $\mathcal{C} \rightarrow Spec (R)$ be a (flat) family of proper, prestable curves where $R$ is a DVR. Suppose the generic fiber is ...
- 8,838
3
votes
2
answers
919
views
How to introduce Kahler differential in category? [closed]
How to define Kahler differential in an abelian category or more general category? Say exact category?
Is there any interesting example?
- 19.9k
4
votes
3
answers
579
views
Average distance between numbers of the form $2^{a}3^{b}$
I want to order all numbers of the form $2^a3^b$. I need to find the average distance between a random consecutive pair.
For example, in case of a random consecutive pair $2^{n'}$ and $2^{n'+1}$, the ...
- 126
4
votes
2
answers
4k
views
Compact Convex sets and Extreme Points
There are examples that show the set of extreme points of a compact convex subset of a locally convex topological vector space need not be closed when the real dimension of the space is at least 3. ...
- 4,060
1
vote
4
answers
2k
views
Is the collection of isomorphism classes of groups a proper class?
The collection of all groups is a proper class, since every set gives rise to a group. But what about the collection of all isomorphism classes of groups? By which argument do I see, that it is a set ...
CommunityBot
- 1
1
vote
0
answers
382
views
Is there functorial point of view to differential operator?
This question is related to differential operator in noncommutative geometry. I wonder whether there is any approach to differential operator that taking differential operator as a functor? I think it ...
CommunityBot
- 1
27
votes
3
answers
2k
views
Using consistency to create new axioms in set theory
As everybody knows, the ZFC axioms may serve as a foundation for (almost)
all of contemporary mathematics, and it is also well-known that several results
are "indecidable" in ZFC, which means that ...
- 236k
12
votes
2
answers
2k
views
What, precisely, is the relationship between "fields of moduli" and "moduli spaces"?
Notation
The term "field of moduli" comes in up in different scenarios, but let's consider the following: Let X->ℙ1 be a G-Galois cover, where everything is over the algebraic closure of ...
CommunityBot
- 1
5
votes
2
answers
5k
views
Sample from uniform distribution vs. Sample from random distribution
I could sample a set of m elements from the uniform distribution over a universe $U$ of n >> m elements. Alternately, I could select a random probability distribution $\mathcal{D}$, and sample $m$ ...
- 28k
13
votes
2
answers
2k
views
Cohomology of rigid-analytic spaces
Let $R$ be a complete discrete valuation ring and let $K$ be its field of fractions. Suppose $X$ is a smooth rigid-anaytic space over $K$. Often it is convenient to have a model of $X$ whose ...
- 11.1k
3
votes
1
answer
225
views
Explicit classifying spaces for crossed complexes
I'm trying to understand the topology behind a certain group which fits into a truncated crossed complex, so I've been trying to understand Brown's construction of the classifying space of a crossed ...
CommunityBot
- 1
0
votes
1
answer
347
views
Where can I learn about master equation?
I am reading a paper by Dorogovstev on structure of growing complex networks with preferential linking. I need to learn master equation for this.
I need a reference for the same.
- 13.6k
9
votes
6
answers
1k
views
When two k-varieties with the same underlying topological spaces isomorphic?
I have a little problem. I'm probably being just so careless..... Here k-varieties are all integral separated k-schemes of finite type over k, where k is a field.
Suppose $X, Y$ are $k$-varieties, ...
- 13.1k
5
votes
3
answers
1k
views
Computation of Joins of Simplicial Sets
It turns out that joins of simplicial sets are fairly easy to define, but hard to manage. In lots of cases, we'd like to compute what a join is, does it look like a horn?, a boundary?, etc? and ...
- 9,627
16
votes
2
answers
3k
views
Number of uniform rvs needed to cross a threshold
Let $N(x)$ be the number of uniform random variables (distributed in $[0,1]$) that one needs to add for the sum to cross $x$ ($x > 0$). The expected value of $N(x)$ can be calculated and it is a ...
- 28k
18
votes
2
answers
1k
views
Deligne-Simpson problem in the symmetric group
Question.
Let $C_1,\dots,C_k$ be conjugacy classes in the symmetric group $S_n$. (More explicitly,
each $C_i$ is given by a partition of $n$; $C_i$ consists of permutations whose cycles
have the ...
CommunityBot
- 1
1
vote
1
answer
188
views
Integral determines function behaviour
Let us define:
$f(t) = t^{-1} \int_{\mathbf{R}^{3}} Exp[-\frac{x^2}{2t}] h(x) dx,$
for a real function h. What can I say about this function if I know that
$f(t) \rightarrow 1$.
I think that the ...
- 9,366
16
votes
2
answers
1k
views
Question about polynomials with coefficients in Z
Let $f = a_0 + a_1 x + \ldots + a_n x^n$ ($f \ne 0$), where $a_i \in \{-1, 0, 1\}$. Let $p(f)$ be the largest number such that $f(x)$ is divisible by $y$ for any integer $x$ and for any $1 \leq y \leq ...
- 156k
2
votes
1
answer
768
views
Foliated bundles and suspensions
Hi,
Is there any criteria, except for the existence of a flat connection, for a foliated bundle $E$ to be a suspension ( a foliated flat bundle)? For example, the Kronecker foliation on the torus is ...
- 8,838
1
vote
2
answers
275
views
Proving if fibres are reduced or not.
Suppose X, Y, Z are k-varieties and $f: X \to Z$ factors through $f': X \to Y$ and $g: Y \to Z$. Suppose all of f, f', g are surjective. Assume that for $z \in Z$, the fibre $f^{-1} (z)$ is reduced. ...
- 13.1k
2
votes
1
answer
197
views
Polytopes related to the conjugation action of a Lie group on multiple copies of itself?
Let G be a finite dimensional real Lie group. As I understand it, the quotient space of G acting on itself by conjugation is a well studied polytope which can be identified with the fundamental alcove ...
- 44.7k
2
votes
3
answers
1k
views
Norm on quotient algebra of a tensor algebra
Suppose you have a finite dimensional real Hilbert space $V$ and you form the tensor algebra
$$T(V) = \mathbb{R} \oplus V \oplus (V\otimes V) \oplus (V\otimes V \otimes V) \oplus \cdots$$
where the ...
CommunityBot
- 1
2
votes
3
answers
2k
views
definition of the set of natural numbers
How can the set $N$ of natural numbers be defined from the point of view of the ZF axiomatic set theory provided the concept of inductive set? Hrbacek-Jech (page 41) says that $N=\{x\in A:\forall(I)(x\...
CommunityBot
- 1
6
votes
0
answers
379
views
ring-valued points of locally ringed spaces
of course, one should expect that the concept of ring-valued points is not well-behaved for locally ringed spaces (LRS). I want to see examples for this.
so consider $LRS \to Set^{Ring}, X \mapsto X(-...
- 63.1k
1
vote
3
answers
1k
views
mean curvature and polar tangential angle
Is it possible to express the mean curvature of a surface of revolution in terms of the first derivative of the polar tangential angle?
To be specific: Let $r=u(\theta)$ be a polar curve in the first ...
- 27.5k
9
votes
1
answer
566
views
algorithm for calculating the Chow groups of a variety over a finite field
Is there an algorithm for calculating the Chow groups of a variety over a finite field?
It is know that $H^{2i,i}_\mathrm{mot}(X,\mathbf{Z}) = CH^i(X)$. In how many cases does this help us?
CommunityBot
- 1
5
votes
1
answer
551
views
What is an exponential?
Is there a notion of exponentiation that subsumes the well known versions, and in particular the versions on
tangent spaces (e.g., of Lie groups and Riemannian manifolds), in which the exponential ...
- 2,756
2
votes
0
answers
165
views
Methods for constructing Frobenius structures
Let ${\mathbb F}:({\mathcal A},{\mathcal E}_{\mathcal A})\to({\mathcal B},{\mathcal E}_{\mathcal B})$ be an exact functor between exact categories, and suppose ${\mathbb F}$ has both a left adjoint ${\...
- 2,756
4
votes
2
answers
336
views
Methods of showing a map has integral or good reduction
Question
Say we have a map, C->D, of relative curves over a Dedekind scheme, S. What are some of the available methods for showing that this map has good reduction, or integral reduction, at some s&#...
- 11.1k
1
vote
1
answer
2k
views
Conditional copulas
Hi,
As part of one of my courses I need to simulate Gaussian, Student-T and Clayton copulas. The only way to do it that I am aware of uses the conditional copulas, so
$$C_{1|2}(u, v) = P[X = F_1^{-1}...
- 4,577
2
votes
1
answer
587
views
Coequalizer in the category of primitive recursive functions
What does a coequalizer in the category of primitive recursive functions look like? I know that in Set, a coequalizer is a minimum congruence but...what is it in particular in the category of ...
- 236k
21
votes
5
answers
4k
views
Isomorphisms of Banach Spaces
Suppose $X$ and $Y$ are Banach spaces whose dual spaces are isometrically isomorphic. It is certainly true that $X$ and $Y$ need not be isometrically isomorphic, but must it be true that there is a ...
- 4,060
1
vote
2
answers
330
views
Relative Frobenius Structure on the Category of G-modules
Let $G$ be a group $H\leq G$ a subgroup of finite index. Further, let ${\mathcal E}^G_H$ denote the class of those short exact sequences of $G$-modules (over some fixed base ring) which split when ...
- 44.7k
8
votes
2
answers
826
views
Weil's theorem about maps from a discrete group to a Lie group.
Let K be a group (with discrete topology), G be a Lie group. Let $\operatorname{Hom}(K,G)$ be the space of all group homomorphisms from K to G. This is a closed subvariety of the space of all the maps ...
- 8,246
2
votes
1
answer
274
views
Algebraic geometric model for symplectic $T^* \Sigma_g$?
I was aware of an algebraic geometric model of symplectic $T^* S^2$ recently, that it is $\{x_1^2+x_2^2+x_3^2=1\}$ in $\mathbb{C}^3$, which the Lagrangian $S^2$ is just the real part, and in this way ...
- 13.2k
-2
votes
1
answer
519
views
cardinal equivalence: for each boolean formula, |quantifications| = |assignments|. [closed]
Cardinal Equivalence Theorem
For each boolean formula, |quantifications| = |assignments|.
The set of valid quantifications has some cardinality, call that |Q(B)...
3
votes
4
answers
699
views
Category of groups = Category of models of group theory?
Is the category of groups with group-homomorphisms the same as the category of models of group theory with elementary maps?
If not so: why?
- 156k
20
votes
1
answer
8k
views
Universal Covering Space of Wedge Products
Today I was studying for a qualifying exam, and I came up with the following question;
Is there a simple description in terms of the subspaces universal covers for the universal cover of a wedge ...
- 56.6k
2
votes
0
answers
357
views
0
votes
6
answers
661
views
Between abstract and concrete: What's the right way to think of specific categories?
At the risk of annoying some of the categorists I feel urged to pose this beginner-ish question:
If one talks about a specific category such as the category of sets with functions or the category of ...
- 1,411
-1
votes
5
answers
594
views
Different Conceptions of Z [closed]
To the algebraist, $\mathbb{Z}$ is just the free group with one generator. To the algebraic topologist, $\mathbb{Z}$ is just the fundamental group of the circle. To be glib, what do $\mathbb{Z}$ mean ...
- 8,532
5
votes
1
answer
315
views
Connections between properties of a group and local symmetries of its Cayley graph
Hi everyone,
Let $\Gamma$ be a finitly generated group.
Does someone know of a connection between properties of $\Gamma$ to local symmetries of its Cayley graph?
More specificly, what can one learn ...
- 12.1k
11
votes
2
answers
2k
views
Teaching and students
Sometimes I get stumped by students' questions in my classes I teach. I am an algebraist by training and have just started teaching. Sometimes I have to teach analysis courses. My question is: Is it ...
CommunityBot
- 1
24
votes
1
answer
3k
views
When does collection imply replacement?
In ordinary membership-based set theory, the axiom schema of replacement states that if $\phi$ is a first-order formula, and $A$ is a set such that for any $x\in A$ there exists a unique $y$ such that ...
- 236k
13
votes
1
answer
709
views
Variants of Waring's problem
Waring's problem (previously asked about here) asks, for each integer $k \ge 2$, what is the smallest integer $g(k)$ such that any positive integer can be written as a sum of $g(k)$ kth powers. We ...
CommunityBot
- 1