Recently Active Questions
159,037 questions
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Induction from split and non-split tori for GL_2 over a finite field
Let k be a finite field, G the k-points of GL_2, T1, T2 the k-points of the split and non-split tori of G.
Then the G-representations C[G/T1] and C[G/T2] are almost the same.
More precisely, they ...
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3
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Where to find nice diagrams of trees and other graphs? [closed]
Are there some publicly available, vector format diagrams of trees and other graphs? They aren't hard to make, but they sure do take a lot of time (for me).
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0
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533
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Two meromorphic functions with overlapping sets of poles
Assume that we have two meromorphic functions $f(z,w)$ and $g(z,w)$, where $z$ and $w$ are complex (we are interested only in behavior on compact sets). Fix $z$ and assume that the sets of poles of $f(...
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What is an example of a function on M_g?
It feels bad talking about a space without knowing a single function on it, hah?
So what is a function on the moduli space of curves, from the geometric point of view?
From the functorial point of ...
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15
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Most helpful heuristic?
What's the most useful piece of mathematical "folk wisdom" you've encountered? I'm talking here about things that aren't theorems, or even conjectures, or even shadows of conjectures -- just broad ...
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1
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Stein Manifolds and Affine Varieties
When is a Stein manifold a complex affine variety? I had thought that there was a theorem saying that a variety which is Stein and has finitely generated ring of regular functions implies affine, but ...
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What are the possible images of a square under an area-preserving map?
Let S be the open unit square in R^2: the set of points (x,y) with 0 < x < 1 and 0 < y < 1. Consider an area-preserving smooth map S --> R^2, that is, a map whose Jacobian has determinant ...
- 4,949
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look into Delzant Polytope
A Delzant polytope in R^n by definition is a simple, rational, and smooth convex polytope in R^n (Ana Cannas da Silva's book for notions.) Do you guys have any insight of the definition, for example, ...
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Resources for getting maths on to the web. [closed]
One thing that came out of Terry Tao's recent blog posts on this matter (first post and follow up) is that it's hard to get an overview of all the different ways of getting one's amazing mathematics ...
- 26.8k
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Reference for iterated homotopy fixed points?
What are (good) references for results about iterated homotopy fixed points? That is, suppose G is a topological group acting on a space (or spectrum) X, and H is a normal subgroup of G. Then one ...
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What happens to Newtonian systems as the mass vanishes?
This question is closely related to another one I asked recently, and may be thought of as a warm-up to that one.
Consider $\mathbb R^n$ with its usual metric, and pick a one-form $b$ and a function $...
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2
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2
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Is the existence of a well-ordering on R independent of ZF?
I am reasonably certain this is the case, but can't find a reference that actually states this, although the Wikipedia article states something close.
- 5,275
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Dolbeault cohomology
Hello
I am trying to get a good book that explains the Dolbeault Cohomology, does anyone know of a good one?
- 56.6k
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answer
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What is the weakest condition on the matrices A_k that guarantees v_k->0 => A_kv_k->0 ? [closed]
What is the weakest condition on the sequence of real matrices A_k that guarantees that whenever a sequence of real vectores v_k converges to zero, the product A_kv_k also converges to zero?
Edit: ...
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1
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Explicit description of a free braided monoidal groupoid with inverses
Let G be a braided monoidal groupoid: it does no harm to suppose that the monoidal product on G is strictly associative, so I'll do that.
"With inverses" means that for every object $X$ of G, there ...
- 25.2k
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Continuous representations G_F \to GL_n(C) are actually continuous for the discrete topology.
Let $F$ be a finite extension of $\mathbb{Q}_p$ and let $\rho\colon G_F \to GL_n(\mathbb{C})$ be a continuous representation, where $G_F$ is the Galois group of $\bar{F}$ over $F$. Then $\rho$ is in ...
- 10.5k
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Notions of degree for maps $S^n \to S^n$?
In algebraic topology, we define a degree for a map $f: S^n \to S^n$ as where the induced map $f_*$ on the $n$-th homology group of $S^n$ sends $1$.
In differential topology, we have a different (...
- 156k
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3
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Are there infinite sets of stellations of polyhedra?
Lists of stellations of polyhedrons are given particular rules like in the book The Fifty Nine Icosahedra which follows "Miller's Rules".
There seems to be no "correct" ruleset to use, so more ...
- 2,615
14
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2
answers
947
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squares in stable homotopy
I noticed that the generator of the second stable stem b is the square of the generator of the first stable stem a, in the sense that if take two copies of a and smash product them together you get b ...
- 3,103
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Graphs with incidence matrices whose pseudoinverses are proportional to their transposes
When I was working on my PhD dissertation, I came across a physical situation involving nodes and flows between them. It turned out that I was working with a complete oriented graph $K_n$ (all nodes ...
- 5,992
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3
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Erdős–Stone theorem type edge density estimates for bipartite graphs?
The Erdős–Stone theorem theory says that the densest graph not containing a graph H (which has chromatic number r) has number of edges equal to $(r-2)/(r-1) {n \choose 2}$ asymptotically.
However, ...
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Smooth unitary irreducible finite-dimensional representations of U(n)
I want to make sure I completely understand the isomorphism classes of smooth unitary irreducible finite-dimensional representations of $U(n)$. We have the irreducible defining representation $R$, and ...
- 156k
5
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1
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435
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Where does the "easy" definition of a weak n-category fail?
Okay, I'm going to ask a naiive question that surely has an interesting answer. So, a first approximation of defining a (small) weak n-category probably goes something like this. Take a pre-n-category ...
- 66.8k
3
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0
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383
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Neglect of Compact Quantum Metric Spaces [closed]
Does anyone have an opinion on Rieffel's theory of compact quantum metric spaces? To me it seems to be a very interesting new area of mathematics. It shows how to generalise complicated geometric ...
- 1,462
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1
answer
258
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9
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4
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778
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SL(2,Z/N)-decomposition of space of cusp forms for Gamma(N)
Since $\Gamma(N)$ is normal in $\mathrm{SL}(2,\mathbb{Z})$, the quotient group $\mathrm{SL}(2,\mathbb{Z}/N)$ acts on the spaces of cusp forms $S_k(\Gamma(N))$. How do these spaces decompose into ...
- 41.4k
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2
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Splitting in triangulated categories
Using the axioms for a triangulated category, is it possible to prove the following:
$A\stackrel{0}{\to}B\to A\oplus B\to$ is a distinguished triangle.
From the first axiom, the map ...
- 8,681
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3
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Is formal proof (formalized mathematics) interesting to practicing mathematicians? To educators? [closed]
Formalizing mathematical proofs so that they can be checked for correctness and manipulated by computer is a recurrent proposal, most notably stated in the QED manifesto (1994). The December 2008 ...
- 12.3k
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2
answers
1k
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Elliptic curve over spectra?
Filling the gaps in my knowledge to understand the tmf question.
So, what is the analogue of elliptic curve over the category of spectra?
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6
votes
3
answers
785
views
Intrinsic characterization of a star shaped domain
Let A be a closed (compact no boundary), embedded (no self intersections), smooth surface of R^3. We say that the interior of A is star shaped if there exists a point p in A, such that for any point q ...
- 28.9k
5
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2
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1k
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Lie Groups and Lie Algebras
What is the exact relationship between Lie groups and Lie algebras? I know it's not bijective because all commutative Lie groups have isomorphic Lie algebras.
- 4,807
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1
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A very very good approximation to Ramanujan constant. Why? [closed]
(2 * 2 * 2 * 3 * 5 * 5 * 5 * 415752385339879101618702506672691517522274861954331757391122938598028498597433207031)^1/5 ~ (very very close to Ramanujan constant)
Would anyone have an idea of why this ...
- 41.4k
4
votes
1
answer
135
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(in-)compatible gradings of an associative algebra tell us...?
If an associative algebra A is $\mathbb{Z}$-graded, then it is automatically $\mathbb{Z}\_2$ (aka $\mathbb{Z}/2\mathbb{Z}$) graded by defining $A\_{\bar{0}}$ to be ...
- 156k
3
votes
2
answers
438
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Flag Varieties - Projective Curves
Is it true that there are no projective curves which are also flag manifolds? If so, why?
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5
votes
3
answers
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Number of paths equal less than equal to a certain length
Hey,
I need to count the number of paths from node $s$ to $t$ in a weighted directed acyclic graph s.t. the total weight of each path is less than or equal to a certain weight $W$. I have an ...
CommunityBot
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-3
votes
2
answers
851
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Cycle Length of the Positive Powers of Two Mod Powers of Ten [closed]
I want to prove that the positive powers of two, mod 10m, cycle with period 4*5m-1. It's simple to prove that the powers of FIVE cycle with this period (2 is a primitive root mod powers of five), but ...
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Stable presentable categories as module categories
There is a theorem of Schwede and Shipley which classifies categories of modules over an A∞ ring spectrum as those stable presentable (∞,1)-categories with a compact generator. Suppose I ...
- 27.2k
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1
answer
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Valuative criterion for properness
Let $f : X \rightarrow Y$ be a finite type morphism of Noetherian schemes. The valuative criterion for properness runs as follows. Suppose that for any DVR $R$ with fraction field $K$ that any $K$-...
- 156k
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1
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Number of Shortest paths problem
Hey,
Is countinng the number of shortest paths in a weighted directed acyclic graph with nonnegative weights #P-complete?
If so, is there a proof I can read somewhere?
Thanks
- 18.6k
6
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1
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Uniformization in algebraic/arithmetic geometry?
Jonah's question makes me wonder: What is with uniformization in algebraic/arithmetic geometry? E.g. this article by Faltings seems to be about that, the Shimura-Taniyama statement too, Mochizuki ...
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3
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2
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341
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Definition modifications without choice
What definitions or equivalencies between definitions for standard set theory objects (such as large cardinals) do not hold or do not carry through in the expected manner to the world without choice? ...
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Can the valuative criteria for separatedness/properness be checked "formally"?
Suppose f:X→Y is a morphism of finite type between locally noetherian schemes. The valuative criterion for separatedness (resp. properness) says roughly that f is a separated (resp. proper) ...
- 24.1k
9
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1
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875
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Analogue of Sperner's lemma for Lefschetz theorem?
Sorry if this is easy/well-known, I don't know much algebraic topology and I'm just curious about this question.
One of the easier proofs of the Brouwer fixed-point theorem (we'll say for n = 2 for ...
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vote
4
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385
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Is it that only with normal matrices, the transition matrix to its [del: inherent] [ins: own] basis is unitary?
Does this even make sense what I translated into english?
PS. I am probably gonna delete this question eventually
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Moment map for toric actions -- online references?
Consider a toric variety, defined as a (normal?) complex projective variety $X$ together with an algebraic action of $(\mathbb C^*)^n$ with finitely many orbits. Now we have two "real symplectic" ...
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2
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Elliptical rotation matrix [closed]
We can rotate a point 'circularly' about an arbitrary axis:
the equation is here, but this site doesn't trust me enough yet to post an image.,
But as we walk theta 0 -> 2PI this takes the point ...
- 9,366
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What representative examples of modules should I keep in mind?
So here's my problem: I have no intuition for how a "generic" module over a commutative ring should behave. (I think I should never have been told "modules are like vector spaces.") The only ...
- 2,992
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a question on function fields
Consider the transcendental extension Q(t) of the field of rationals.
To Q(t) adjoin the root of the polynomial x^5+t^5=1. The resulting
field Q(t)[x] is a radical extension of Q(t). Is it true that ...
CommunityBot
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12
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2
answers
2k
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Non-quasi separated morphisms
What are some examples of morphisms of schemes which are not quasi separated?
- 11.3k
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Adapting families of diffeomorphisms to an open cover
Has anyone seen the following result in the literature? I've asked a few experts but so far I've come up with nothing.
Given a manifold M and an open cover {U_i} ...
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