21
votes
2answers
733 views

Profinite groups as étale fundamental groups

Does every profinite group arise as the ├ętale fundamental group of a connected scheme? Equivalently, does every Galois category arise as the category of finite ├ętale covers of a connected scheme? ...
7
votes
2answers
945 views

What are the different theories that the motivic fundamental group attempts to unify?

I must preface by confessing complete ignorance in the subject. I've read introductory texts about the theory of motives, but I am certainly no expert. In ...
44
votes
9answers
9k views

Galois Groups vs. Fundamental Groups

In a recent blog post Terry Tao mentions in passing that: "Class groups...are arithmetic analogues of the (abelianised) fundamental groups in topology, with Galois groups serving as the analogue of ...