Extended \'etale homotopy groups from profinite Galois categories
classification
🧮 math.AG
keywords
etalegroupshomotopyprofiniteextendedgaloisshapecategories
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In this note we show that the protruncated shape of a spectral $\infty$-topos is a delocalization of its profinite stratified shape. This gives a way to reconstruct the extended \'etale homotopy groups (i.e., the non-profinitely complete \'etale homotopy groups) of a coherent scheme from its profinite Galois category.
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