Hello, This question might be vague and not thought-through enough. If we have a real positive number $x$, we can start to write it as a continued fraction: $x = a_0 + \frac{1}{x …

I frequently talk to people who think of finite fields as arithmetic analogs of punctured discs. This makes some sense: the absolute Galois group of a finite field is the profinite …

What is the cohomological dimension of the braid group $\mathcal{B}_n$ on n-strands ? A reference would be appreciated.

Or equivalently, if $G$ is a group, do the projective and injective dimension of $Z$ (viewed as a $ZG$-module) agree? Thanks!

Given a sheaf $\mathcal{F}$ with respect to some Grothendieck topology, is the cohomological dimension for this sheaf less than or equal to the cohomological dimension of a finer t …

Let $\ell$ be a prime number and let $f:X \to Y$ be a morphism of schemes of finite type over the complex numbers (or a regular scheme of dimension at most 1, in which $\ell$ is in …