Let $X$ be an anabelian curve over a number field $K$ and let $p:Y\rightarrow X$ be a finite etale cover. Then is anything known (or has anything been conjectured) about the field …

Proving things suspected to be true in anabelian geometry is usually very hard. Maybe it is easier to disprove things suspected to be false? In particular, I am interested in fals …

Grothendieck calls a "discretification" of a profinite group $\hat G$, a discrete group $G$ whose profinite completion is isomorphic to $\hat G$. Does Grothendieck also define a …

Let $X$ be an integral proper normal curve over a (perfect) field $F$, of genus $\geq 2$. One variant of Grothendieck's "section conjecture" states that the sections $G_F \rightarr …

I had probed friends of mine about Grothendieck's motivation for making the anabelian geometry conjectures, and they gave me the following explanation: If $X$ is a hyperbolic curv …

A while back, J. Ellenberg brought the following problem to my attention. If $G$ is a residually finite group, let $\widehat G$ be its profinite completion. Let $S$ be a closed su …