# 2021-05-13

## 00:14

• $$\pi_1(X)$$ can be defined for schemes, see etale fundamental group.
• What are the higher homotopy groups of schemes? #todo/questions
• What do they measure?
• More fundamentally, what do higher homotopy groups of spheres measure about $${\mathsf{Top}}$$ at all??
• What are the Eilenberg-MacLane spaces in $${\mathsf{Sch}}$$?
• What are the Moore spaces in $${\mathsf{Sch}}$$?
• There should be an axiomatic characterization of these coming from model categories
• What are the “spheres” for $${\mathsf{Sch}}$$?
#web/quick-notes #todo/questions