Questions tagged [reference-request]
This tag is used if a reference is needed in a paper or textbook on a specific result.
14,574
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Weak topology on subsets of a normed space
I have few questions about the subsets of a normed space $X$ endowed with the weak topology. Let $E$ be such subset.
When is the norm a continuous function on $E$?
When is the metric induced by the ...
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1
answer
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Classification of Hopf-Galois Extensions as Torsors
Faithfully flat Hopf-Galois extensions of rings: $A\to B$, with $H$ coacting on $B$ such that $B\otimes_AB\simeq B\otimes H$, are often thought of as being accessible substitutes for $G$-torsors in ...
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Have topographs been studied before?
This is my first post on MO so I hope this question is suitable. I have quite a few definitions which I will need to state before my questions at the end of this post. Please let me know if anything ...
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5
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Proof that no differentiable space-filling curve exists
Could someone provide a reference or a sketch of a proof that no differentiable space-filling curve exists?
Or piecewise differentiable?
Must every continuous space-filling curve be nowhere ...
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answer
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Identities for power series like $\sum_n z^{n^3}$
Probably, one of the first power series that every mathematician encounter is the geometric series
$$\sum_{n=0}^\infty z^n = \frac1{1-z}, \quad z \in \mathbb{C},\; |z| < 1 .$$
Also, a particular ...
user40023
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7
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number theory which is close to analysis
I have basic training in Fourier and Harmonic analysis. And wanting to enter and work in area of number theory(and which is of some interest for current researcher) which is close to analysis.
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3
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Counting number of points in a lattice with bounded length
I am interested in counting number of lattices using the following theorem.
The following is Theorem IV (page 412) in Chapter VIII of "An introduction to the geometry of numbers (second printing, ...
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2
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Reference for proof that consistency of $\omega_1$-Erdos cardinal implies Con(Chang's Conjecture)
What is a good source for Silver's proof (or a more modern version) that Con($\exists \omega_1$-Erdos cardinal) implies Con(Chang's Conjecture)?
Silver's original proof seems to have never been ...
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Does the higher cohomology of a quasi-coherent sheaf on a Stein manifold vanish?
It is a well-known result in algebraic geometry that if $X$ is an affine scheme and $\mathcal{F}$ is a quasi-coherent sheaf on $X$, then the higher cohomologies of $\mathcal{F}$ vanish, i.e.
$$
H^i(X,\...
- 8,707
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6
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Thales' semicircle theorem in higher dimensions
Thales semicircle theorem says that an angle inscribed in a semicircle is a right angle.
Q1. Does a cone with apex on a hemisphere and encompassing the circular base
have a solid angle ...
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Square-free sieve over number fields
I am trying to work on extending various methods to study square-free values of polynomials (or more generally, $k$-free values) over general rings of integers, and a literature review has yielded ...
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Is there a generalization of Polya urns to continuous outcome event?
Take for example the simplest model where there are n blue balls and m white balls in an urn. Then, in a first step realization, a white one has been drawn and then c + 1 of this colour had been put ...
- 163
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orbit space of $\mathbb{Z}_p$ action over complex projective space by permuting the homogeneous coordinates
$Z_p$:=cyclic group of order $p$.
I want to understnd $H_\ast(\mathbb{C} P^{n}/Z_{n+1};Z)$ with $(n+1)$ being a prime number,and the action is given by permuting the homogeneous coordinates.
For ...
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Texts about Dwork's work
I want to ask about references to papers, that probably exist, which explain the articles of Bernard Dwork starting from "The rationality of the zeta function of an algebraic variety" to "On the ...
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Combinatorics of palindromic decompositions
This is sort of a companion to my question Number of trivializations of a trivial word in the free group (which in turn is motivated by my earlier question here). It turns out that that question may ...
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Is the derived category of perfect complexes idempotent complete?
Let $\mathcal{C}$ be a category. We call a morphism $\alpha: X\rightarrow X$ an idempotent if $\alpha^2=\alpha$ in $\mathcal{C}$. We call $\mathcal{C}$ is $\textit{idempotent complete}$ if any ...
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Are there any algebraic geometry theorems that were proved using combinatorics?
I'm collaborating with some algebraic geometers in a paper, and when writing the introduction I mentioned the interaction of combinatorics and algebraic geometry, and gave some examples like the ...
2
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answers
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Localized eigenfunctions of drift Laplacians
I am looking for literature which discusses localization of eigenfunctions of drift Laplacians, i.e. $L\underline u=-\Delta \underline u+\underline{v}.\nabla \underline u$ in 2D/3D domains with ...
- 21
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Cyclic structure on a balanced (or ribbon) monoidal category
As it is well known, a balanced (and in particular ribbon) monoidal category is an algebra over the framed little 2-discs operad. The latter is homotopy equivalent to the operad of moduli space of ...
- 8,244
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maximum principle on compact manifolds with boundary
Let us consider the equation $Lu + f(u) = 0$ on a compact manifold $\overline{M} = M \cup \partial M$ with boundary, with Dirichlet boundary conditions. $L$ is a linear elliptic operator, and $f$ ...
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References for the bicategory of ring-bimodule pairs
One of the standard examples of a bicategory is the bicategory of rings (with bimodules as 1-morphisms), which is sometimes denoted $\operatorname{Bim}$ and in other sources $\operatorname{Ring}$ (or $...
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Source for equations involving congruences of Fibonacci and Lucas numbers
In a paper of Cohn (see here), he uses some formulae involving congruences of Lucas- and Fibonacci-numbers (equations 11,12,13 in the preliminaries section). Does anyone know a source for these (and ...
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Differential forms along the fiber
Let $E \to M$ be a smooth fiber bundle. Instead of differential forms defined on the whole tangent bundle $TE$ one could also consider forms on the vertical tangent bundle $VE$, i.e. forms defined on ...
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1
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Hermitian form, fundamental $2$-form of Kahler structure on $\mathbb{C}^n$
I've come across the following (it is an excerpt of Stolzenberg's lecture notes 19):
Wirtinger's Inequality.
Let $L$ be a complex linear space and let $M$ be a real
even-dimensional subspace....
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votes
1
answer
421
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Formal definition of arithmetic transfinite recursion
Recently I have been trying to find the definition of the subsystem $ATR_0$ of second-order arithmetic. Only "definitions" I have found were quite vague, like informal definition on Wikipedia which ...
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Notions of/References for freely generated (symmetric) monoidal categories
We often describe a category by giving a (directed, multi-)graph and freely generating a category of paths. I would like to know to what degree this intuition generalizes to monoidal categories, and ...
- 21
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$\Gamma$ cohomology of principal series
Let $G$ be a noncompact connected real semisimple Lie group with finited center. Let $\Gamma$ be a cocompact discrete subgroup of $G$, and let $P$ be a parabolique subgroup
with Langlands ...
- 1,091
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1
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Nested convex optimization
Suppose I have a convex optimization problem of the form $$\min_x f(x) ~~s.t.\\x\in X$$. Say that $f(x)$ and its (sub)gradient are not given in a closed form, but are determined by solving a convex ...
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Notation: Categories of measur(abl)e spaces
Is there a common notation in the literature for
the category of measurable spaces and measurable maps?
the category of measure spaces and measure-preserving maps?
The nlab suggests $\mathsf{Measble}...
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1
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Subclass of semimartingales for which all characteristics can be estimated?
I'm going to ask the question for Ito semimartingales rather than semimartingales in general, but more general answers would be great.
An Ito semimartingale is a martingale for which the ...
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Mal'cev "rational equivalence" and model theory
In Universal Algebra, it is possible to say that two presentations denote the "same" kind of algebraic structures, if the two corresponding varieties are "rationally equivalent" (Mal'cev 1958).
In ...
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Addition law for elliptic curves of the form $x^2y^2+a(x+y)+b=0$
Did anybody consider addition law for elliptic curves of the form $$x^2y^2+a(x+y)+b=0\,?$$ Does this form have any specific name?
- 11.9k
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What is the "type" of a contact vector field?
Let $(M,\theta)$ be a $(2n+1)$-dimensional contact manifold, $\mathcal{C}=\ker\theta$ the contact distribution, and $X\in\mathcal{C}$ a vector field belonging to $\mathcal{C}$.
In a couple of minor ...
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When do we have $D_{\text{perf}}(\text{Qcoh}(X))\simeq D_{\text{perf}}(X)$?
Let $(X,\mathcal{O}_X)$ be a scheme (or more generally a ringed space). We know that in general the derived category of complexes of quasi-coherent modules $D(\text{Qcoh}(X))$ is not equivalent to the ...
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Why Jacobson, but not the left (right) maximals individually?
I firstly asked the following question on MathStackExchange a couple of months ago. I did not receive any answers, but a short comment. So, I decided to post it here, hoping to receive answers from ...
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answers
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Residual scheme to local complete intersection schemes in the projective space
Let $A$ be an integral Noetherian $\mathbb{C}$-algebra. Denote by $\mathbb{P}^3_A:=\mathbb{P}^3_{\mathbb{C}} \times_{\mathbb{C}} \mathrm{Spec}(A)$. Let $X,Y$ be closed local complete intersection ...
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Obtain any 3-manifold from repeating surgeries on knots in $S^3$
In Witten's “QFT and Jones Polynomials” paper, page 383, it states that: "It is a not too deep result that every 3-manifold can be obtained from or reduced to $S^3$ (or any other desired 3-manifold) ...
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$K_0$ of integral group ring of cyclic group $\mathbb{Z}/p\mathbb{Z}$
Is there a table for the computation of $K_0(\mathbb{Z}[\mathbb{Z}/p\mathbb{Z}])$?
These groups are also known as ideal class group in number theory.In topology,they are the home of some important ...
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2
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An alternative definition of pseudo-coherent complex
Let $(X,\mathcal{O}_X)$ be a scheme or a general ringed space. First recall that a complex of $\mathcal{O}_X)$-modules $\mathcal{E}^{\bullet}$ is called strictly perfect if $\mathcal{E}^{\bullet}$ is ...
- 8,707
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Looking for a theorem that says that the embedding $H^{1-\sigma}(M)\subset C^1(M)$ is compact for $\sigma\in (0,1)$
I am Looking for a theorem that says that the embedding $H^{1-\sigma}(M)\subset C^1(M)$ is compact for $\sigma \in (0,1)$, where $M$ is a compact manifold.
Any references are appreciated.
PS
I am ...
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Is $\mathcal M _{g,n}$ anabelian?
Are the moduli spaces $\mathcal M _{g,n}$ expected to be anabelian? Is there anything known in that direction?
Thank you very much for your help in any case!
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2
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Centralizers of reflections in special subgroups of Coxeter groups
Let us consider a (not necessarily finite) Coxeter group $W$ generated by a finite set of involutions $S=\{s_1,...,s_n\}$ subject (as usual) to the relations $(s_is_j)^{m_{i,j}}$ with $m_{i,j}=m_{j,i}$...
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2
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Ivanov's metaconjecture on surface homeomorphisms
In Fifteen problems about MCG Ivanov stated the following metaconjecture:
Every object naturally associated to a surface S and having
a sufficiently rich structure has $Mod(S)$ as its groups of ...
- 1,703
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0
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Is there some absoluteness between the Boolean valued universe $V^{B}$ and $V$?
It is well known that if $\phi$ is a $\Delta_{1}$-formula and $x_{1},..,x_{n}$ in $V$ and $V[G]$ is a forcing extension, then $V\models\phi(x_{1},...,x_{n})$ if and only if $V[G]\models\phi(x_{1},...,...
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Riemannian simplicial complex and quasi-conformal complex
In this paper by Robert Young, the author defines
We define a riemannian simplicial complex to be a simplicial
complex with a metric which gives each simplex the structure of a riemannian
...
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Vector Bundles of small rank
I recently started the study of vector bundles on $\mathbb{P}^n$, and started to read Rao's article 'A family of vector bundles on $\mathbb{P}^3$'. There, there is a notion of spectrum of a vector ...
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Reference for multivariate orthogonal polynomials
I want to learn about multivariate orthogonal polynomials. Is there a good textbook/survey that you could suggest? I need to see common examples like Jack's polynomials etc .. and also general ...
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Morgan Shalen compactification of $\mathbb C^2$
I'm reading the Otal's survey on the compactification of Morgan Shalen.
(available here)
He claims in an example (page 8) that the compactification of $\mathbb C^2$ is $S^4$, which sounds completely ...
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1
answer
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Frey's Formula and utilisation of the Hasse Invariant in "Links between Stable elliptic curves and Diophantine equations."
In the paper "Links between Stable elliptic curves and Diophantine equations" for an elliptic curve $E$ with normal Weierstrass form $$y^2 = x^3 -g_2x -g_3$$ with $g_i \in \mathbb{Z}$ w.l.o.g. Then ...
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1
answer
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Tail inequality for orthomartingales/martingale difference random fields
It is known that if $(S_i= \sum_{j \leqslant i }X_i, \mathcal F_i)$ is a martingale,
then for each
$
\beta>1$, $\delta\in (0,\beta-1)$ and $\lambda>0$, and each integer $N \geqslant 1$, the ...
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