All Questions

Let $\mathbb{A}$ denote the ring of adeles of $\mathbb{Q}$, let $\mu$ be the Haar measure of $\mathbb{A}$, and let $\|\cdot\|_{\infty}$ denote the sup-norm of the components in the Archimedean of $\...

I already asked this on math.stackexchange.com, but did not receive much responses. I hope this is also appropriate for mathoverflow. In the paper Homological algebra on a complete intersection, with ...

i. Apply the definition of modular equivalence and write down what $ p^{-1}p ≡ 1 (mod \, q)$ means ii. Rearrange what you get and apply Bezout’s identity to conclude that if $gcd(p, q) = 1$ then $p−1 ...

Famously, there are arbitrarily long arithmetic progressions $x$, $x+y$, ..., $x+ky$ consisting of primes, by Green-Tao. I was wondering whether the following generalization is also known (by the same ...

Let $X$ be an $n$-dimensional CW-complex and let $A \subseteq X$ be a subcomplex. I want to show that the quotient space $X/A$ admits a structure of a CW-complex with skeletons $(X/A)^j := \pi(X^j \...

Question. Let $X$ be a scheme. Let $\mathcal{E}$ be a sheaf of $\mathcal{O}_X$-modules. Is there always a quasicoherent sheaf $\mathcal{E}'$ together with a monomorphism $\mathcal{E} \to \mathcal{E}'$?...

If $X$ is a connected, compact metric space with distance function $d : X^2 \rightarrow \mathbb{R}^+$, is it true that there exists a positive real number $a$, dependent on $X$ and $d$, such that for ...

Let $f: {\bf Z} \to {\bf R}$ be a finitely supported function on the integers ${\bf Z}$. I am interested in knowing when there exists a finitely supported non-negative function $g: {\bf Z} \to [0,+\...

Question: What are some natural examples of recursive pseudowellorderings? By natural, I mean in the style of reasonable ordinal notation systems as opposed to dependent on a Gödel numbering or an ...

Consider the following parametric linear problem: \begin{align} \min z(t)=c^T x\\ Ax=b(t)\\ 0\leq x\leq u. \end{align} We know $z(t)$ is a piecewise linear function. Let $x(t_1)$ and $x(t_2)$ be the ...

In a review seminar today, I heard the speaker takes the below for granted, but I have no enough background "Yang-Mills (YM) instantons in 4D can be naturally identified with (i.e. have the same ...

I wonder if the following inequality involving skew symmetric matrices is true: Suppose that $B,C \in \mathbb{R}^{d \times d}$ are skew-symmetric matrices, and $\Sigma \in \mathbb{R}^{d \times d}$ ...

This is an attempt to make my relation between bordism invariants in $d$ and $d+2$ dimensions, following a previous attempt more explicit. This counts as a different question, since some more specific ...

Consider an $m$-by-$n$ matrix $A$ with entries in a field $k$; we can see $A$ as a point in the affine space $\mathbb{A}^{m n}$. The rank of $A$ will be $\leq r$ (where $r<\min(m,n)$) if and only ...

In Drinfeld's paper "Hopf algebras and the quantum Yang-Baxter equation" there is a statement (Theorem 2) that Yangian is a unique quantization of the corresponding Lie bialgebra. My question is ...