It happens a lot of times that when one defines a new object (ring, module, space, group, algebra, morphism, whatever) out of given data one first chooses some additional structure …

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 $E$ …

This question comes from the same place as my other one. In reading SGA 4 1/2, but not SGA4 itself (at least, not the obvious sections xv + xvi), one can learn about the "cospecia …

Given an action of a group $G$ on a topological space $X$, the associated homotopy quotient is $$X_G := (EG \times X)/G,$$ where $EG$ is the total space of a universal principal $G …

For "$n=1$" the answer is "yes." A group is abelian iff its generators commute. Let $G_0=G$ be a group and let it be generated by $X_0=X$. For each $n>0$ let $G_n=[G_{n-1},G_{n- …

The quick definition of a map $f \colon X \to B$ of schemes being acyclic is that the natural unit of adjunction $\def\id{\operatorname{id}}\id \to f_* f^*$ is an isomorphism, wher …

Dear mathoverflowers. Just wondering if the following inequality is true. For all $ p >1$ there is some $C$ such that $ | |x+1|^p-|y+1|^p -p(x-y)| \le C ( |x|+|y| + |x|^{p-1} …

I know the construction of a 3D topological quantum field theory (TQFT) from a modular tensor category. I heard that we can even (mathematically) construct 4D TQFT from a modular …

Hi Guys, We have a d-regular bipartite Graph $G = (X,Y,E)$ with $|X| = |Y| = n$ and $|E| = nd$. i want to know a Upper Bound of the number of Matching Thankx

Let $ \Omega $ be an open and bounded subset of $ \mathbb{R^n} $, and let $ f:\Omega \to \mathbb{R} $ be a continuous function. I'm looking for some (preferably, minimal) condition …

Yitang Zhang recently published a new attack on the Twin Primes Conjecture. Quoting Andre Granville: “The big experts in the field had already tried to make this approach w …

for example, x is random variable, f(x) and g(x) are two "very very" different distribution functions. It is impossible to calculate variance analytically, so if we want to compare …

Assume that $f$ is (Euclidean) $L-$biLipchitz mapping of the unit circle onto a triangle $\Delta(A,B,C)$. Can we find a $10000 L$ bi-lipchitz extension of $f$ onto the whole plane. …

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 …

I'm not sure wether or not the following sum uniformly converge on $\mathbb{R}$ : $$\sum_{n=1}^{\infty} \frac{\sin(n x) \sin(n^2 x)}{n+x^2}$$ Can someone help me with it? (I can' …