Let $X$ ad $Y$ be (noetherian) schemes and let $\mathcal I \subseteq \mathcal O_Y$ be a sheaf of ideals on $Y$. Let $f \colon X \to Y$ be a morphism of schemes. In general the shea …

Hi, I was wondering about the following question: if you have a faithful action of a group G on the real line R by orientation-preserving homeomorphisms, it is easy to construct …

I am trying to determine the number of paths between two points. I am representing the paths as a list of steps "ruru" = right -> up -> right -> up For my purposes, we can assume …

Let $p=2^a-1>7$ be a Mersenne prime and so $a$ is an odd prime. Can we say that $(p^2+1)/2$ is not equal to the square of a prime number? Many thanks for your help BHZ

Is it true that for a given nonnegative number, there exists a measure-theoretical entropy value (supremum of entropies of all partitions under a measure-preserving transformation) …

Suppose I have the symmetric tridiagonal matrix: $ \begin{pmatrix} a & b_{1} & 0 & ... & 0 \\ b_{1} & a & b_{2} & & ... \\ 0 & b_{2} & a …

I wanna prove following equation $ \sum_{i=1}^n \prod_{k=1,k\neq i}^n \prod_{j=1,j\neq k}^{n+1}(x_j - x_k) = -\prod_{i=1}^n \prod_{j=1,j\neq i}^n (x_j - x_i) $ I have verified sev …

In section 5 in "The entropy formula for the Ricci flow and its geometric applications" Grisha Perelman has written: Fix a closed manifold $M$ with a probability measure $m$, and …

Iwaniec and Kowalski, in their famous book Analytic Number Theory states a strong form of the effective Chebotarev density theorem page 143, and prove it assuming both GRH for Arti …

I am interested in finding a canonical general expression for the area of a spherical polygon in $\mathbb{S}^2$ knowing the side lengths of the polygon and a bound on the internal …

Although I know that "ZFC & there exists a measurable cardinal" and "ZFC & there exists a real-valued measurable cardinal" are equiconsistent with one another, I am not sur …

Let $E$ be the smallest set of functions $\mathbb{N}^+\to\mathbb{N}^+$ containing the identity function $n \mapsto n$ and closed under exponentiation $(f,g) \mapsto \left(n \mapst …

I've read   @TauMu's question   about the set of functions   $\mathbb N\rightarrow\mathbb N$   generated from the identity map by repeatedly applying exponentia …

This question is about the space of all topologies on a fixed set X. We may order the topologies by refinement, so that τ ≤ σ just in case every τ open set is open …

There are several occasions in the study of dynamical systems that are called phase transitions. For example the parameters $t$'s where the pressure $P(f,t\phi)$ fail to be $C^k$ …