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Results tagged with etale-covers
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user 43054
14
votes
Accepted
Do higher etale homotopy groups of spectrum of a field always vanish?
The étale topos of a field $k$ is just the topos of sets with a continuous $\mathrm{Gal}(k)$-action (here continuous is equivalent to all stabilizers being open), hence it is the colimit (in the ∞-cat …
- 16.5k
18
votes
Accepted
Are higher etale homotopy groups topological groups in a natural way?
TL;DR The higher étale homotopy groups are the homotopy groups of the profinite completion of the shape of the étale topos. As such they are profinite groups. If you choose to see profinite groups as …
- 16.5k