A note on Gersten’s conjecture for étale cohomology over two-dimensional henselian regular local rings

Makoto Sakagaito

doi:10.5802/crmath.9

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 Sakagaito ¹

¹ Indian Institute of Science Education and Research, Mohali

Comptes Rendus. Mathématique, Volume 358 (2020) no. 1, pp. 33-39.

Résumé
Abstract

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.

Reçu le : 2019-04-30
Révisé le : 2019-09-17
Accepté le : 2019-12-17
Publié le : 2020-03-18

DOI : 10.5802/crmath.9

Affiliations des auteurs :

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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