This tag is used if a reference is needed in a paper or textbook on a specific result.

**2**

votes

**0**answers

119 views

### 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 ...

**3**

votes

**1**answer

104 views

### 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 ...

**5**

votes

**0**answers

238 views

### 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 ...

**-2**

votes

**0**answers

131 views

### About “covering” subgroups

Let $H$ be a subgroup of $S_n$ (the symmetric group with n elements). In the paper I read (cf. Thm 3.17 there), the authors define $H$ to be a covering if the following condition holds: for all ...

**15**

votes

**5**answers

2k views

### 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 ...

**20**

votes

**0**answers

318 views

### 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 ...

**8**

votes

**6**answers

1k views

### 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.
...

**3**

votes

**0**answers

124 views

### 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, ...

**6**

votes

**2**answers

150 views

### 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 ...

**3**

votes

**0**answers

152 views

### 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.
$$
...

**15**

votes

**5**answers

726 views

### 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 ...

**1**

vote

**0**answers

82 views

### 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 ...

**4**

votes

**0**answers

57 views

### 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 ...

**1**

vote

**3**answers

251 views

### 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 ...

**6**

votes

**2**answers

357 views

### 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 ...

**7**

votes

**0**answers

127 views

### 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 ...

**3**

votes

**1**answer

141 views

### 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 ...

**16**

votes

**7**answers

1k views

### 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**

votes

**0**answers

44 views

### 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 ...

**5**

votes

**0**answers

54 views

### 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 ...

**1**

vote

**0**answers

58 views

### 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 $f$ ...

**2**

votes

**0**answers

91 views

### 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 ...

**1**

vote

**1**answer

78 views

### 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 ...

**4**

votes

**1**answer

233 views

### 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 ...

**0**

votes

**1**answer

156 views

### 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 ...

**1**

vote

**1**answer

90 views

### 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 ...

**2**

votes

**0**answers

65 views

### 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 ...

**1**

vote

**0**answers

48 views

### $\Gamma$ 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**

vote

**1**answer

53 views

### 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 ...

**3**

votes

**1**answer

321 views

### 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 ...

**1**

vote

**0**answers

52 views

### 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 ...

**2**

votes

**1**answer

184 views

### 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 ...

**3**

votes

**1**answer

200 views

### 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?

**2**

votes

**1**answer

138 views

### 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 ...

**4**

votes

**0**answers

153 views

### 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 ...

**5**

votes

**1**answer

323 views

### Why Jacobson, but not the left (right) maximals individually?

I firstly asked the following question on MathStackExchange, but I did not receive any responses, but a short comment. So, I decided to post it here, hoping to receive answers from experts.
...

**2**

votes

**0**answers

78 views

### 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 ...

**0**

votes

**0**answers

28 views

### On a remark regarding to initial-boundary elliptic estimate

In the paper "On the motion of the free surface of a liquid" see [CL], the authors proved the initial boundary elliptic estimate (proposition 5.28)
$$
||\nabla^r q||_{L^{2}(\Omega)}+||\nabla^{r-1} ...

**12**

votes

**4**answers

386 views

### 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) ...

**0**

votes

**0**answers

43 views

### Control of Hessian by its trace in a bounded domain

We know if $u:\mathbb{R}^n \to \mathbb{R}$ is a smooth function with compact support, then we can show, via integration by parts, that
$$
\|\Delta u\|=\|\nabla^2u\| \tag 1
$$
where $||\cdot||$ is ...

**4**

votes

**1**answer

249 views

### $K_0$ 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 ...

**2**

votes

**1**answer

97 views

### 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 ...

**0**

votes

**0**answers

25 views

### Orbifold metric and ample line bundle

Let $X$ be a complex projective variety with only orbifold singularities, and $L$ be an ample line bundle on $X$. Is there a K\"{a}hler metric in the orbifold sense representing the first Chern class ...

**2**

votes

**1**answer

42 views

### 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 ...

**5**

votes

**1**answer

332 views

### 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!

**4**

votes

**2**answers

151 views

### 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 ...

**4**

votes

**1**answer

210 views

### 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 ...

**4**

votes

**0**answers

204 views

### 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 ...

**0**

votes

**0**answers

29 views

### 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
...

**0**

votes

**1**answer

120 views

### 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 ...