Recently Active Questions
159,036 questions
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Can the objects of every concrete category themselves be realized as small categories?
More precisely, is every concrete category C isomorphic to a category C' of small categories such that the morphisms between two elements of C are precisely the functors between their images in C'?
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Is there a software package that does Schubert Calculus computations?
Is there a good software package for doing computations in the cohomology ring of Grassmannians? Things like, I can write down a polynomial in, in fact, special Schubert classes, but it's one where ...
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Representablity of Cohomology Ring
I know that the individual cohomology groups are representable in the homotopy category of spaces by the Eilenberg-MacLane spaces. Is it also true that the entire cohomology ring is representable? If ...
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Chains intersecting antichains in finite posets
I feel a little embarrassed to be asking this question here, since I think it should be much easier than I'm making it, but here goes:
Given a finite poset P, does there necessarily exist some chain ...
- 18.6k
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Explicit convergence of Baker-Campbell-Hausdorff
Let g be a finite dimensional simple Lie algebra over C. The Baker-Campbell-Hausdorff series defines a (multivariable) analytic function from a neighborhood of 0 in g \times g \to g. What is the ...
- 7,800
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proving that an inclusion map from a subcomplex is a homotopy equivalence
This is a pretty basic question but I have been stuck on it for a while.
Given an abstract simplicial complex X and a subcomplex A, why does * suffice to show that the map |A|->|X| induced by ...
- 52.7k
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Given a sequence defined on the positive integers, how should it be extended to be defined at zero?
This question is inspired by a lecture Bjorn Poonen gave at MIT last year. I have ideas of my own, but I'm interested in what other people have to say, so I'll make this community wiki and post my ...
- 118k
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Dance battles and de Bruijn sequences
I hope this doesn't fall under the "not interesting to mathemeticians" category.
I'm attempting to solve one of the facebook engineering puzzles. Essentially, the idea is that two dancers do a ...
- 2,615
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Pontryagin product from an operad
For a topological group G, we have a Pontryagin product in homology by multiplying representative cycles. This gives the homology the structure of an associative graded algebra. Am I correct in ...
- 52.7k
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Example where you *need* non-DVRs in the valuative criteria
The valuative criterion for separatedness (resp. properness) says that a morphism of schemes (resp. a quasi-compact morphism of schemes) f:X→Y is separated (resp. proper) if and only if it ...
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What is an example of a topological space that is not homotopy equivalent to a CW-complex?
It would also be nice if someone can explain this comment appearing on the Wikipedia page on CW-complexes:
"The homotopy category of CW complexes is, in the opinion of some experts, the best if not ...
- 27.5k
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Weil-Châtelet group
Sorry if this is obvious. I'd like to understand why the map
WC(E/Q) -> H^1(Gal(Q/Q), E(Q))
is bijective. Thanks.
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Change of basis with Multilinear fucntion [closed]
Take a multi-linear function(or functional) M that takes m arguments V1…Vm, each with a dimension n. Consider only the case where m=n. Let there be a change of basis performed on the arguments(V1...Vm)...
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Gaussian curvature and mean curvature. [closed]
Define Gaussian curvature for a nonorientable surface. Can you define mean curvature for a nonorientable surface?
- 27.5k
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Smooth immersion(?) of graphs into the plane
Sorry if the terminology's wrong, I don't know differential topology. Also, this is more of a brain-teaser than a bona fide research question, but it's hopefully a "real mathematician"-level brain-...
- 14k
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Order of an automorphism of a finite group
Let G be a finite group of order n. Must every automorphism of G have order less than n?
(David Speyer: I got this question from you long ago, but I don't know whether you knew the answer. I stil ...
- 8,681
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Latex Template for a Popular Math Journal [closed]
Can anyone offer a Latex template for a popular mathematics journal? It is easy to prepare a template for a technical journal with simple page layout but what I am looking for is something like the ...
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Limit of sequence involving gamma functions
Let G be the gamma function, and b be a constant in (-2,inf). Let
H(n, i) = G(i+1+b) * G(n-i+1+b) / [G(i+1) * G(n-i+1)]
for integers n > i > 0. Let
S(n) = \sum_{i=1}^{i=n-1} H(n, i).
Let x_ n = H(...
- 10.5k
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Kato's log motives
What are they and what are their intended uses? Does anyone have notes/slides of this talk?
I am curious about "log motives" because there seems to exist a "log motivic yoga" among experts in ...
- 10.8k
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Legendrian homotopy of curves in a contact structure?
I'm aware of the great body of work on Legendrian knot theory in contact geometry, but suppose I'm curious just about homotopy and not isotopy. How does one understand the space of Legendrian loops ...
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Friedberg, Insel, and Spence Linear Algebra example
In the chapter 6.4 on normal and self-adjoint operators, there is an example of an infinite dimensional inner product space H that has a normal operator but that has no eigenvectors.
The space is the ...
- 5,992
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Embedding abelian categories to have enough projectives
Is it true that the pro-objects of an abelian category form a category with enough projectives?
In general, given an abelian category A, is there a canonical way to embed it a bigger abelian ...
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Logarithmic structures on moduli of elliptic curves over Z
I've heard it stated that if you take the moduli of elliptic curves with some level structure imposed (as a moduli scheme over Spec(Z)), there is a logarithmic structure that you can impose at the ...
- 45.7k
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Are there any criteria for a presheaf which is an etale sheaf to be a sheaf in the fppf topology?
I am happy to hear answers to variants too. For instance, my situation I actually have a sheaf in the smooth topology.
CommunityBot
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Limit Linear Series
A linear series on a curve C is a line bundle L together with a subspace V of the global sections of L. Eisenbud and Harris develeoped a theory of limit linear series which explans how (L, V) ...
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Sums of cubes and more
It's well-known that every natural number can be written as a sum of 4 squares of integers.
Has there been any recent progress about the similar problem for the cubes, 4-th powers and so on? I ...
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Model category structures on categories of complexes in abelian categories
Section 2.3 of Hovey's Model Categories book defines a model category structure on Ch(R-Mod), the category of chain complexes of R-modules, where R is a ring. Lemma 2.3.6 then essentially states (I ...
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When and how is a group of order n isomorphic to a regular subgroup of equal order?
In "Group Theory and Its Application to Physical Problems" by Morton Hamermesh, Morton states Cayley's theorem: Every group G of order n is isomorphic with a subgroup of the symmetric group Sn, which ...
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Dualizing sheaf on singular curves
I am trying to understand the stabilization map, which takes a prestable curve (a curve with some marked points, and at worst nodal singularities) and returns a stable curve (a curve with some marked ...
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What is the difference between the Power Law and Zipf's Law?
I am new to statistics. Could somebody tell me what is the difference between a Power Law and Zipf's Law. The latter could be just for texts but I cant see any difference in their essence.
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What is the "right" hermitian structure on tensor products of quantum group representations?
This is pretty specific, but there are some experts around.
So, in Chari & Pressley, it's explained that in the standard *-structure, every irreducible, finite-dimensional representation of a ...
- 44.7k
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What's the sense in which A_\infty algebras are "deformable"?
I realise this is a very vague question! I've heard people say that A∞ algebras are the right homotopy-theoretic generalization of usual associative algebras, because you can deform them. What ...
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Is there an example of a scheme X whose reduction X_red is affine but X is not affine?
For Noetherian schemes this follows from Serre's criterion for affineness by a filtration argument.
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Stack with affine stabilizers but not quasi-affine diagonal
Give an example of a stack X with affine stabilizer groups and separated but not quasi-affine diagonal.
Remarks:
1) If X has finite stabilizer groups then the diagonal is quasi-finite and separated, ...
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Points of a weakly locally separated algebraic space
If X is a quasi-separated algebraic space and Spec k -> X is an etale presentation, then X is isomorphic to Spec k' for a field k'. (This is also true if X is Zariski locally quasi-separated.) The ...
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Ignore this question [closed]
This question is a hacky way to create some tags for you to use. Move along.
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