Let $X$ be a smooth and projective variety over a field of characteristic zero. Let $Y$ be a normal variety, with finite quotient singularities (an orbifold!) and let $\pi: Y \to X …

I have recently been slogging my way through Shelah's "Large continuum, oracles". Essentially from the start there has been a question needling me which I cannot seem to answer. …

This is related to my question Adelic description of moduli of $G$-bundles on a curve. Let $X$ be a smooth, projective, and geometrically connected curve over a finite field $\mat …

It is often used implicitly that the maps which associate to metrics curvature quantities (Riemann, Ricci, scalar curvature) and Differential operators like the Laplacian are analy …

So, any line bundle $L$ on an abelian variety $X$ determines a type $(d_1,\ldots,d_g)$ where $d_i|d_{i+1}$. It's well known that if $d_1\geq 3$ then $L$ defines an embedding, that …

This is actually not a question of mine, so I'll be short on motivation and say nothing beyond that if this were true, a few fancy harmonic analysis techniques that a colleague of …

My question is as follows: Let $k$ be a field of characteristic zero and let $\overline{k}$ be an algebraic closure. Let $V$ be an algebraic variety over $k$ and let $\overline …

Could anybody please advice me, how to show that nondegenerate bilinear form with property $f(u,v)=-f(v,u)$ on vector space $V$ exists iff $dim V = 2l$?

They had plenty of time to adopt the theory of categories. They had Eilenberg, then Cartan, then Grothendieck. Did they feel that they have established their approach already, that …

It is known that $[L^p(0,T;H)]^* = L^q(0,T;H^*)$. If $p=q=2$ and $H$ is a Hilbert space, is there an easier proof to show that the spaces are isometric? The proof that I know for …

Hurwitz's theorem on automorphisms tells us that the group of automorphisms of a nonsingular complex algebraic curve of genus at least 2 is bounded above by $84(g-1)$ where $g$ is …

Proposition: If $F$ is a field, let $F[x]$ be the ring of all polynomials whose coefficients are in $F$. The fraction field of $F[x]$, denoted $F(x)$, is defined to be the ratios $ …

What are some techniques and theorems of analytic number theory that have proved useful outside of number theory?

In Gromov's paper "volume and bounded cohomology"1982 http://scholar.google.com.hk/scholar?hl=zh-CN&q=volume+and+bounded+cohomology&btnG=&lr= .As a step for proving tha …

Maybe one of the strange things about quantum mechanics comes from the mental dificulty of reconciling the fact that a system in a superposition of several states, when measured or …