# All Questions

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### Can an abelian variety/Q have no points over Q_sol?

Let $A/\mathbb{Q}$ be an abelian variety. Must there be a finite solvable extension $K/\mathbb{Q}$ such that $A(K)$ is nontrivial? This follows from the conjecture that the maximal ...
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### Probability of non-negative matrix relaxation

Given matrix $M\in\Bbb\{0,1\}^{n\times n}$, take $\mathscr{M}[M]=\{Q\in R_{\geq0}^{n\times n}:Q[ij]>0\iff M[ij]=1\}$. Does ...
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### flatness and derived completion

Let $A$ be a local ring of maximal ideal $\mathfrak{m}$. Let $\hat{A}$ be its completion. If $A$ is noetherian , then we know that $A\rightarrow\hat{A}$ is faithfully flat. If $A$ is not noetherian, ...
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### Non-Forcing and Independence

I asked this question about two weeks ago on MSE and haven't gotten an answer, so I thought I would post the question here. Do there exists sentences which are independent of ZFC, cannot be shown to ...
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### Relative nonarchimedean disks and annuli

Let $A$ be a Huber (i.e. f-adic) ring, meaning a topological ring with an open subring $A_0$ which is adic and has finitely generated ideal of definition. Is there a good notion of closed disk of ...
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### What does this graph notation mean? E\S [on hold]

I am studying graph theory right now but I am confused what E\S means where both E and S are sets of edges. What does the "\" indicate?
1answer
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### Unitary representation with fixed Casimir

Let $G$ be a connected reductive real Lie group with Lie algebra $\mathfrak{g}$. We denote by $\widehat{G}_u$ the unitary dual, that is the set of isomorphism classes of unitary reprensentation of ...
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### Prove an equation is always false [on hold]

How can I prove an equation is always false? For example: b = b + 1 is false for all values of b. Very simple to see. Now given a more complicated equation, such as: b = sin(sin(b) - .56)) ...
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There is a problem when I'm reading a paper. Equation: $min_p|p-p^*|^2+\alpha |R(p)|^2 + \beta |D(p)-\delta|^2$, where $p, p^*, R(p), D(p), \delta$ are all $M\times N$ matrices, and $p^*, R(), D(), ... 1answer 96 views ### Symmetry type of non-cohomological automorphic forms By Katz-Sarnak philosophy a family of$L$-functions would have a symmetry type which would reflect the statistics of$L$-functions, such as low lying zeros and moments. Shin-Templier's paper on ... 5answers 562 views ### On an example of an eventually oscillating function For$x\in(0,1)$, put $$f(x):=\sum_{n=0}^{\infty}(-1)^{n}x^{2^{n}}.$$ This function possesses interesting properties. It grows monotonically from$0$up to certain point. Then it starts to oscillate ... 0answers 54 views ### Inductive/Projective Limits of Topological Algebras It is common to form inductive/projective limits of Banach/Frechet spaces in order to come up with natural topologies for common vector spaces. For instance, For$k \ge 0$and$K_n$compact ... 0answers 118 views ### When does a perverse sheaf occur in the decomposition theorem? Suppose I am in the setting of the decomposition theorem, i.e., we have the decomposition of the direct image$f_*\mathbb Q_\ell$, where$f:X\to Y$is proper. Then the direct image decomposes into a ... 0answers 10 views ### How to test the significance of covariance [on hold] I'm using the Mutual Informacion covariance in RNA sequences and I want to know if there exits a way to test if some covariance is significant, let's say, an associated p-value. Thanks to all for ... 0answers 14 views ### Combining the output of two functions smoothly for a droplet effect [on hold] I'm trying to write a function which generates this droplet effect implicitly. I've got a function which generates both of the shapes and I'm looking for a way to somehow combine these two in such a ... 1answer 116 views ### Degree of a rational function [on hold] I would like to have the (simplest) proofs for the following theorem (there may be more than one interesting approach): Let$f=\frac{p}{q}:\mathbb{C}\longrightarrow\mathbb{C}$be a quotient of ... 2answers 363 views ### How close to an integer can a polynomial root be? Suppose I have a polynomial$p(x) = a_n x^n + ... + a_0$where$a_n, \dots, a_0$are integers. I would like to show that any root of this polynomial is either an integer or is far from an integer. ... 1answer 42 views ### Maximizing Frobenius Norm of Commutator (an opposite Procrustes problem) I was wondering if anybody has any suggestions on the following problem: Let$S$be an$n\times n$positive definite symmetric matrix. I wish to find an$n\times n$orthogonal matrix$R$which ... 1answer 139 views ### Why can we not always take a Kähler class to be in rational cohomology? Given a Kähler manifold$(X,\omega)$we know that its Kähler class lies in an open cone of$H^{1,1}(X) \cap H^2 (X,\mathbb{R})$. Since$\mathbb{Q}$is dense in$\mathbb{R}$we should be able to find a ... 0answers 33 views ### Partially ordered set [on hold] Show that a subset$C$of a preordered space$(X, ≤)$is a chain if and only if$C × C ⊂ A ∪ A^{−1}$, where$A := \{(x, y) : x ≤ y\}$,$A^{−1} := \{(x, y) : (y, x) ∈ A\}$. 0answers 27 views ### Upper and Down Bound,directed,cofinal [on hold] I'm learning a partially ordered set.Can you give me some example of each these definition: 1.Upper and Down Bound : ... 0answers 70 views ### Can you give me some example of each these definition [on hold] I'm learning a partially ordered set.Can you give me some example of each these definition: 1.Upper and Down Bound : ... 0answers 67 views ### every(ultra)filter on set I is principle if and only if I is finite [on hold] 1)the filter generated by{a,b} is not ultra filter? 2)the filters generated by singleton are precisely the principle ultrafilters. 3)every(ultra)filter on set I is principle if and only if I is ... 1answer 77 views ### Base of a cone in a vector space: can one always choose a convex base? Let$C$be a pointed convex cone in a vector space$V$. This means that$C$satisfies the three following axioms:$C + C \subset C$,$\mathbb{R}_+ \cdot C \subset C$, and$C \cap (-C) = \{ 0 \}$. ... 0answers 49 views ### izomorphism of finite abelian group [on hold] Please help me with rezolving this problem from Romanian "Gazeta Matematica" : "an finite abelian group G have |End G | and |Aut G | coprime numbers. Show that |G| is square free. Thank you! 1answer 51 views ### Decomposition of semi simple local systems I found A question similar to this, but the answer wasn't clear to me and I'm not supposed to ask for further clarification in the answer section. Let$L$a semi simple local system defined over an ... 0answers 48 views ### Optimal covering Let consider a problem of optimal covering of Hamming space. So we have Hamming space$\{0,1\}^n$and some integer$r$. We want to find a set$A \subseteq \{0,1\}^n$such that any point from ... 0answers 33 views ### Summation of Geometric Series [on hold] Im really desperate please help!!! how can you show that a. the sum oscillates between the two values a and b for the summation of geometric series {a*r^(n-1)}` provided that this is divergent? ... 1answer 66 views ### Finiteness properties for graph of groups decompositions My curiosity was raised by the following question and the huge variety of comments and suggestions it attracted. I wondered if a converse statement might be equally interesting. Let$G$be a finitely ... 0answers 22 views ### Interchange summation and differentiation [migrated] I asked this question already on math.stackexchange, but did not receive any answers see here Let$f = \sum_{n=0}^{\infty} a_n e_n $where$e_n$are an ONB of$L^2[0,1].$Now assume we have that ... 1answer 87 views ### Covering finite groups by kernels Let$G$be a finite group. When does there exist a finite group$H$such that every$h\in H$is in the kernel of some epimorphism$H\to G$? This is well-known to be true for$G$abelian, for example ... 0answers 42 views ### Summation of geometric series divergence [on hold] The summation of some geometric series a*r^(n-1) is divergent. But what i don't understand is this: If the summation of a geometric series is divergent, then one of its sum is: a. the sum oscillates ... 0answers 117 views ### Octonions product: inversion in the right and identity in the left Once octonions product is studied, together with the relations with$Spin(8)$and$SO(8)$geometry (see for instance Robert Bryant's notes), one realises that the key fact bringing all the phenomena ... 0answers 59 views ### Asymptotic expansion square root matrix I am looking for an asymptotic expansion for$\underline\gamma$which is the "square root" matrix of a symmetric$p\times p$matrix$\gamma$. Here$\underline\gamma\$ is assumed to be symmetric, e.g. ...

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