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]
Sakagaito, Makoto1
1 Indian Institute of Science Education and Research, Mohali
Comptes Rendus. Mathématique, Tome 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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DOI : 10.5802/crmath.9
Sakagaito, Makoto 1

1 Indian Institute of Science Education and Research, Mohali 
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Sakagaito, Makoto. A note on Gersten’s conjecture for étale cohomology over two-dimensional henselian regular local rings. Comptes Rendus. Mathématique, Tome 358 (2020) no. 1, pp. 33-39. doi : 10.5802/crmath.9. http://www.numdam.org/articles/10.5802/crmath.9/

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