Geodesic
Nonabelian ${{H}^{1}}$ and the Étale Van Kampen Theorem
Canadian journal of mathematics, Tome 63 (2011) no. 6, pp. 1388-1415

Voir la notice de l'article provenant de la source Cambridge

DOI

Generalized étale homotopy pro-groups $\pi _{1}^{\acute{e}t}(C, x)$ associated with pointed, connected, small Grothendieck sites $(C, x)$ 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 $\pi _{1}^{\acute{e}t}(\acute{e}t(X) x)$ , a description of Grothendieck's short exact sequence for Galois descent in terms of pointed torsor trivializations, and a new étale van Kampen theorem that gives a simple statement about a pushout square of pro-groups that works for covering families that do not necessarily consist exclusively of monomorphisms. A corresponding van Kampen result for Grothendieck's profinite groups $\text{ }\!\!\pi\!\!\text{ }_{1}^{\text{Gal}}$ immediately follows.
DOI : 10.4153/CJM-2011-030-x
Mots-clés : 18G30, 14F35, étale homotopy theory, simplicial sheaves 
Misamore, Michael D. Nonabelian ${{H}^{1}}$ and the Étale Van Kampen Theorem. Canadian journal of mathematics, Tome 63 (2011) no. 6, pp. 1388-1415. doi: 10.4153/CJM-2011-030-x
@article{10_4153_CJM_2011_030_x,
     author = {Misamore, Michael D.},
     title = {Nonabelian ${{H}^{1}}$ and the {\'Etale} {Van} {Kampen} {Theorem}},
     journal = {Canadian journal of mathematics},
     pages = {1388--1415},
     year = {2011},
     volume = {63},
     number = {6},
     doi = {10.4153/CJM-2011-030-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2011-030-x/}
}
TY  - JOUR
AU  - Misamore, Michael D.
TI  - Nonabelian ${{H}^{1}}$ and the Étale Van Kampen Theorem
JO  - Canadian journal of mathematics
PY  - 2011
SP  - 1388
EP  - 1415
VL  - 63
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2011-030-x/
DO  - 10.4153/CJM-2011-030-x
ID  - 10_4153_CJM_2011_030_x
ER  - 
%0 Journal Article
%A Misamore, Michael D.
%T Nonabelian ${{H}^{1}}$ and the Étale Van Kampen Theorem
%J Canadian journal of mathematics
%D 2011
%P 1388-1415
%V 63
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2011-030-x/
%R 10.4153/CJM-2011-030-x
%F 10_4153_CJM_2011_030_x

Cité par Sources :