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 of definition of ...
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 false generalizations of ...
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 notion of the ...
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 $G_F \rightarrow \pi_1(X)$ of the ...
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 curve over some field ...
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 surface of genus $g ...