Unanswered Questions
50,302 questions with no upvoted or accepted answers
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Commuting totalizations with filtered colimits in the plus-construction for $\infty$-presheaves on a topological space
Let $\mathrm{An}$ be the $\infty$-category of anima (i.e., $\infty$-groupoids).
Let $X \colon \mathcal{O}(U)^{\mathrm{op}} \to \mathrm{An}$ be a presheaf on a topological space $U$.
Now, consider a ...
- 7,876
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Hasse principle for rational number times a quadratic form
Motivation:
Hasse principle for rational times square
local-global principle for units
Does the Hasse norm theorem easily imply the global squares theorem?
Let $K/F$ be a quadratic extension of global ...
- 41
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Applicability of Besicovitch Covering Theorem in different norms in $\mathbb{R}^n$
This question is probably quite simple, but I would still appreciate a straightforward answer, whether positive or negative. Thank you in advance.
I alredy know that the Besicovitch Covering Theorem ...
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Kashiwara-Schapira Stack of microsheaves
I will assume familiarity with the notions of singular support as defined by Kashiwara and Schapira in Sheaves on Manifolds. Let $M$ be a manifold, one can define a functor :
$\mu Sh^{pre} : Op_{T^*M, ...
- 111
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90
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Dirichlet series of $\zeta'(s)\zeta'(1-s)$
I want to find the Dirichlet series coefficients of $\zeta'(s)\zeta'(1-s)$.
I know that $$\zeta'(s)=-\sum_{n=1}^{\infty}\frac{\log n}{n^s},$$provided $\Re(s)>1$. I would have thought it would be ...
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What is known about the algebras $\mathrm{End}_{U_q(\mathfrak{sl}_2)}(L(d)^{\otimes n})$?
Let $A_{d,n}=\mathrm{End}_{U_q(\mathfrak{sl}_2)}(L(d)^{\otimes n})$. For $d=1$, this is the Temperley-Lieb algebra $A_{1,n}=TL_n(q+q^{-1})$. For $d=2$, Scrimshaw calls this the tangle algebra, first ...
- 502
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Nonnegative submartingales: convergence to infinity in probability
Consider a nonnegative submartingale $X_n$, with uniformly bounded jumps, and jump variance uniformly bounded from below. Can we conclude that it converges to infinity in probability? Also, is it ...
- 1,907
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Algorithm that allows to get any value of A000123 if finite number of values of A002577 are known
Let
$T(n,k)$ be an integer coefficients such that $$ T(n,k) = \begin{cases} 1 & \text{if } k = 0 \vee n = k \\ \displaystyle{ \sum\limits_{i=k-1}^{n-1} T(n-1,i) T(i,k-1) } & \text{otherwise} \...
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Factorization of polynomials vanishing on quadrics: divisibility by the defining equation
Let $P(x,y,z)$ be a real polynomial that vanishes on the ellipsoid defined by $$ g(x,y,z) := \frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} - 1 = 0.$$ How can one rigorously justify the ...
- 2,573
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Equivalent definitions of volume of representations (or characteristic classes of flat bundles)
Statement of the problem:
Let $M$ be a closed connected oriented manifold with fundamental group $\Gamma$ (considered as covering transformations acting on its universal cover). Let $G$ be a (...
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From global to local: strong failure of regularity (quasirandomness) in random bipartite graphs
Let $n$ be a positive integer and $\varepsilon > 0$ with $\varepsilon \ll 1$ and $n \gg 1/\varepsilon$. Let $G = (A, B, E)$ be a bipartite random graph with $|A| = |B| = n$, where each edge between ...
- 66k
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Fejér-Riesz inequality for $H^p$ on the unit disk for more general curves
Let us consider the Hardy space $H_p$ on the unit disk, and a function $f \in H_p$. There's an inequality by Fejér and Riesz stating that:
\begin{equation}
\int_{-1}^{1} |f(x)|^p \, dx \leq \frac{1}{2}...
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Projective module over Robba ring
Is a projective module finitely generated over Robba ring free?
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Can we have a descending powerset class in Stratified ZF?
Working in $\sf Stratified \ ZF + Class \ Comprehension$, where class comprehension is that of Morse-Kelley. Is there anything to forbid having a class $C$ that meet these two conditions:
$\forall x \...
- 12.4k
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Is there a model category structure for C-homotopy?
After reading Harry Altman's question about homotopy with regards to arbitrary connected spaces I started wondering about the extent to which the notion defined there is compatible with more recent ...
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