Geodesic
The adic tame site
Documenta mathematica, Tome 26 (2021), pp. 873-945 Cet article a éte moissonné depuis la source EMS Press

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For every adic space X we construct a site Xt​, the tame site of X. For a scheme X over a base scheme S we obtain a tame site by associating with X/S an adic space Spa(X,S) and considering the tame site Spa(X,S)t​. We examine the connection of the cohomology of the tame site with étale cohomology and compare its fundamental group with the conventional tame fundamental group. Finally, assuming resolution of singularities, for a regular scheme X over a base scheme S of characteristic p>0 we prove a cohomological purity theorem for the constant sheaf Z/pZ on Spa(X,S)t​. As a corollary we obtain homotopy invariance for the tame cohomology groups of Spa(X,S).
DOI : 10.4171/dm/832
Classification : 14F20, 14F35, 14G17, 14G22
Mots-clés : positive characteristic, tame ramification, Grothendieck topology 
@article{10_4171_dm_832,
     author = {Katharina H\"ubner},
     title = {The adic tame site},
     journal = {Documenta mathematica},
     pages = {873--945},
     year = {2021},
     volume = {26},
     doi = {10.4171/dm/832},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/832/}
}
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Katharina Hübner. The adic tame site. Documenta mathematica, Tome 26 (2021), pp. 873-945. doi: 10.4171/dm/832

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