I am considering the problem of determining the algebraic independence of $n$ polynomials in $m$ variables with real coefficients, where $m \geq n$. The variables will be denoted b …

Hi all, Suppose that $\mathbf{f}=[f_1, f_2,\ldots,f_m]$ and $\mathbf{g}=[g_1,g_2,\ldots,g_m]$ are two $m$-dimensional vectors. All $f_i$'s are chosen uniformly randomly from a fin …

Let $G$ be a commutative algebraic group stack over $\mathbb{F}_q$ (I don't really care about the precise definition: I'm secretly thinking about the Picard stack of a projective c …

I have a function f(x,n) can be expressed as a cubic function of x with coefficients that are functions of n. For example x^3 + (n-2)x^2 + (3n-6)x + n. I want to prove that for e …

Hello, I have the question, which should has an easy answer, but I do not see that: To find a short exact sequence $0 \to A \to B \to C \to 0$ of abelian groups (where each homomo …

Does a connected finite locally free group scheme G over a scheme S of characteristic p>0 has degree a power of p? I know that when S is the spectrum of a field k, it is true. So …

Let $X$ be a normal complex affine algebraic variety. Suppose that $Y$ is an open subvariety of $X$, and that the codimension of $X\setminus Y$ in $X$ is at least $2$. One version …

Ground field $\Bbb{C}$. Algebraic category. Elliptic surfaces are those surfaces endowed with a morphism onto some smooth curve, with generic fiber an elliptic curve. Suppose $E$ …

Let $p$ be a prime integer, and let $(\mathbb Z/p\mathbb Z)^*$ be the set of non-zero elements of $\mathbb Z/p \mathbb Z$. Denote by $S((\mathbb Z/p \mathbb Z)^*)$ the group of per …

Hi there, I have a question somehow related to a previous question of mine http://mathoverflow.net/questions/131157/fundamental-cycle-separators-and-crossing-numbers. Consider a …

Let $M$ and $N$ be finite dimensional smooth manifolds. A smooth map $f: M \to N$ is an embedding if and only if there is an open neighborhood $U$ of $f(M)$ in $N$ and a smooth ma …

How to find the value of root (6 +root(6+root(6+.....) ?

According to the wiki of Kakutani's fixed-point theorem, A set-valued mapping $\varphi$ from a topological space $X$ into a powerset $\wp(Y)$ called upper semi-continuous if for ev …

A five digit number is formed using the digits 1,3,5,7,9 without repeating any one of them.How to find the sum of ll of them?

On a board having 8 rows and 6 columns find the number of squares that can be made?