Extended étale homotopy groups from profinite Galois categories (1812.11637v2)

Abstract: 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.