MathOverflow

Let $X$ be some projective variety, and $\mathcal{F}$ be some coherent sheaf on $X$ with nonfree locus of high codimension. Is it possible to construct some finite map $f:Y\to X$ such that $f^*\mathcal{F}$ (modulo torsion) is actually a vector bundle...

The following simple-looking inequality for complex numbers in the unit disk generalizes Problem B5 on the Putnam contest 2020:
Theorem 1. Let $z_1, z_2, \ldots, z_n$ be $n$ complex numbers such that $\left|z_i\right| \leq 1$ for each $i \in \left\{1,2,\ldots,n\right\}$. Prove that\begin{align}\left| z_{1} + z_{2} + \cdots + z_n - n \right|\geq\left| z_{1} z_{2} \cdots z_n -...

Numerical evidence suggests that all complex zeros residing in the critical strip $0 < \Re(s) < 1$ of:
$$\frac{\Gamma(s)}{z}Li_s(z) \, \pm \, \frac{\Gamma(1-s)}{z}Li_{1-s}(z)$$
are on the critical line $\Re(s)=\frac12$ for all $z \lt 1$ (with both individual terms $\ne 0$, except when $z=-1$)....

Greetings to everyone at MOF. I am a very beginning student of mathematics, and one of the reasons I study mathematics on my own is that I could not find an answer to a simple question: "How can one perfectly compare two subsets of natural numbers?"...