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- W1968823235 abstract "Generalized etale homotopy pro-groups $pi_1^{ets}(mc{C}, x)$ associated to pointed connected small Grothendieck sites $(mc{C}, x)$ are defined and their relationship to Galois theory and the theory of pointed torsors for discrete groups is explained. Applications include new rigorous proofs of some folklore results around $pi_1^{ets}(et{X}, x)$, a description of Grothendieck's short exact sequence for Galois descent in terms of pointed torsor trivializations, and a new etale van Kampen theorem which gives a simple statement about a pushout square of pro-groups that works for covering families which do not necessarily consist exclusively of monomorphisms. A corresponding van Kampen result for Grothendieck's profinite groups $pi_1^{Gals}$ immediately follows." @default.
- W1968823235 created "2016-06-24" @default.
- W1968823235 creator A5036761252 @default.
- W1968823235 date "2010-02-18" @default.
- W1968823235 modified "2023-09-27" @default.
- W1968823235 title "Nonabelian $H^1$ and the 'Etale van Kampen Theorem" @default.
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