Article ID Journal Published Year Pages File Type
8897563 Journal of Pure and Applied Algebra 2018 19 Pages PDF
Abstract
We generalize toposic Galois theory to higher topoi. We show that locally constant sheaves in a locally (n−1)-connected n-topos are equivalent to representations of its fundamental pro-n-groupoid, and that the latter can be described in terms of Galois torsors. We also show that finite locally constant sheaves in an arbitrary ∞-topos are equivalent to finite representations of its fundamental pro-∞-groupoid. Finally, we relate the fundamental pro-∞-groupoid of 1-topoi to the construction of Artin and Mazur and, in the case of the étale topos of a scheme, to its refinement by Friedlander.
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Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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