00:14
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\(\pi_1(X)\) can be defined for schemes, see etale fundamental group.
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What are the higher homotopy groups of schemes? #todo/questions
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What do they measure?
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More fundamentally, what do higher homotopy groups of spheres measure about \({\mathsf{Top}}\) at all??
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What are the Eilenberg-MacLane spaces in \({\mathsf{Sch}}\)?
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What are the Moore spaces in \({\mathsf{Sch}}\)?
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There should be an axiomatic characterization of these coming from model categories
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What are the “spheres” for \({\mathsf{Sch}}\)?