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

Makoto Sakagaito

doi:10.5802/crmath.9

Number Theory, Homological Algebra

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

Makoto Sakagaito ¹

¹ Indian Institute of Science Education and Research, Mohali

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

Abstract
Résumé

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.

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.

Received: 2019-04-30
Revised: 2019-09-17
Accepted: 2019-12-17
Published online: 2020-03-18

DOI: 10.5802/crmath.9

Author's affiliations:

Makoto Sakagaito ¹

¹ Indian Institute of Science Education and Research, Mohali

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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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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