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162,007 questions
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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 ...
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What Are Some Naturally-Occurring High-Degree Polynomials?
To construct J. H. Conway's look-and-say sequence, begin by putting down a 1 as the first entry. The other entries are found by saying the previous entry aloud, and writing what you hear.
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Hyperplane sections of general type surfaces
Let $X$ be a smooth projective complex surface with $K_X$ very ample. Let $D\in |K_X|$ be a general element.
Does there exist another smooth projective variety $D'$ with a finite flat morphism $D\to D'...
- 156k
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Stubborn p-Cartesian edge in higher topos theory
In the situation of lemma 2.4.2.7 in higher topos theory, Lurie has an inner fibration $p : X \rightarrow ∆^2$ with $X$ a simplicial set and he uses the fact that an edge $g$ covering $∆^{\{0,1\}}$ is ...
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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 ...
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Condition under a function is uniquely identifiable by the supremum values
Let $f(x),g(x)$ be two real-valued functions on $\mathbb{R}$ and $h(x,y)$ be a real-valued function on the plane. We can assume continuity (maybe piecewise differentiability also) of these functions. ...
- 62.9k
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Intersections of strict transform and strict transform of intersections
Let $Z_1,Z_2$ and $Y$ be subvarieties of a locally complete intersection variety $X$ over $\mathbb C$.
Consider the strict transforms of $Z_1$ and $Z_2$ in the blowup $Bl_YX$, the question is: when ...
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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, ...
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Categorical structure guaranteed to exist, but not necessarily preserved
Background
I'm currently studying arithmetic universes (AUs), which are defined to be list-arithmetic pretoposes (see "Joyal's arithmetic universe as list-arithmetic pretopos" by Maietti). ...
- 68k
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When is −∥x−y∥+∥A(x−y)∥ a CPD kernel ? - Difference of CPD radial kernels remains CPD (Bernstein functions)
I’m studying a family of translation-invariant kernels built from two norms and would like to understand exactly when their difference remains conditionally positive-definite. In particular, we focus ...
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Constructing the Stone space of a distributive lattice
Does anyone have a good reference for the method of giving a topology to a distributive lattice as outlined in M.H. Stone's "Topological representation of distributive lattices and Brouwerian ...
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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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Hartman uniform distribution of means
Background: for a discrete abelian group $G$, a character of $G$ is a homomorphism $\chi:G\to \mathbf S^1$, $\mathbf S^1$ being the circle group $\{z\in \mathbb C:|z|=1\}$ with ordinary multiplication....
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Determinant inequality involving Hermitian, positive definite matrices
Let $A,B,C\in M_{n}(\mathbb C)$ be Hermitian, positive definite matrices such that $A+B+C=I_{n}$. Show that
$$ \det \left( 6 \left( A^3 + B^3 + C^3 \right) + I_n \right)\ge 5^n \det \left( A^2 + B^2 + ...
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