Hypercovers in topology

Daniel C. Isaksen; Daniel Dugger

Hypercovers in topology

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arxiv math/0111287 v1 pith:4LHUS4IC submitted 2001-11-27 math.AT

Daniel Dugger , Daniel C. Isaksen This is my paper · ORCID

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keywords topologicalcomplexconstructequivalencefactfieldsfunctorshocolim

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We show that if U is a hypercover of a topological space X then the natural map from hocolim U to X is a weak equivalence. This fact is used to construct topological realization functors for the A^1-homotopy theory of schemes over real and complex fields.

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Unstable motivic and real-\'etale homotopy theory
math.AG 2025-01 conditional novelty 8.0 of 10

Real etale motivic homotopy theory over a scheme S is equivalent to sheaves of spaces on the real spectrum of S, and on pointed connected motivic spaces the real etale localization is the rho-telescope.

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