The adic tame site
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...
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| Main Author: | |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2021
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| In: |
Documenta mathematica
Year: 2021, Volume: 26, Pages: 873-945 |
| ISSN: | 1431-0643 |
| DOI: | 10.25537/dm.2021v26.873-945 |
| Online Access: | Resolving-System, lizenzpflichtig, Volltext: https://doi.org/10.25537/dm.2021v26.873-945 Verlag, lizenzpflichtig, Volltext: https://elibm.org/article/10012113 
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| Author Notes: | Katharina Hübner |
MARC
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| 520 | |a 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). | ||
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