Comptes Rendus
no. 1
Théorie des nombres, Algèbre homologique
A note on Gersten’s conjecture for étale cohomology over two-dimensional henselian regular local rings
[Une note sur la conjecture de Gersten pour la cohomologie étale sur des anneaux locaux réguliers henséliens à deux dimensions]
Makoto Sakagaito1
1 Indian Institute of Science Education and Research, Mohali
Comptes Rendus. Mathématique, Volume 358 (2020) no. 1, pp. 33-39.

Nous montrons la conjecture de Gersten pour la cohomologie étale sur des anneaux locaux réguliers henséliens sans supposer de caractère équicaractéristique. En application, nous obtenons le principe local-global pour la cohomologie de Galois sur des anneaux locaux henséliens à deux dimensions de caractéristique mixte.

We prove Gersten’s conjecture for étale cohomology over two dimensional henselian regular local rings without assuming equi-characteristic. As an application, we obtain the local-global principle for Galois cohomology over mixed characteristic two-dimensional henselian local rings.

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Révisé le :
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DOI : 10.5802/crmath.9
Makoto Sakagaito 1

1 Indian Institute of Science Education and Research, Mohali
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     author = {Makoto Sakagaito},
     title = {A note on {Gersten{\textquoteright}s} conjecture for \'etale cohomology over two-dimensional henselian regular local rings},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {33--39},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {1},
     year = {2020},
     doi = {10.5802/crmath.9},
     language = {en},
}
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Makoto Sakagaito. A note on Gersten’s conjecture for étale cohomology over two-dimensional henselian regular local rings. Comptes Rendus. Mathématique, Volume 358 (2020) no. 1, pp. 33-39. doi : 10.5802/crmath.9. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.9/

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[10] Ivan A. Panin The equicharacteristic case of the Gersten conjecture, Tr. Mat. Inst. Im. V. A. Steklova, Volume 241 (2003) no. 2, pp. 169-178 | MR | Zbl

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[12] Makoto Sakagaito On problems about a generalization of the Brauer group (2016) (https://arxiv.org/abs/1511.09232v2)

[13] Makoto Sakagaito On a generalized Brauer group in mixed characteristic cases (2019) (https://arxiv.org/abs/1710.11449v2)

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