A note on Gersten’s conjecture for étale cohomology over two-dimensional henselian regular local rings
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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| Format: | Article |
| Language: | English |
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Académie des sciences
2020-03-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.9/ |
| _version_ | 1827785235259981824 |
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| author | Sakagaito, Makoto |
| author_facet | Sakagaito, Makoto |
| author_sort | Sakagaito, Makoto |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T16:17:17Z |
| format | Article |
| id | doaj.art-6a8db046470b4629b919ff1fc724dbe9 |
| institution | Directory Open Access Journal |
| issn | 1778-3569 |
| language | English |
| last_indexed | 2024-03-11T16:17:17Z |
| publishDate | 2020-03-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj.art-6a8db046470b4629b919ff1fc724dbe92023-10-24T14:19:10ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692020-03-013581333910.5802/crmath.910.5802/crmath.9A note on Gersten’s conjecture for étale cohomology over two-dimensional henselian regular local ringsSakagaito, Makoto0Indian Institute of Science Education and Research, MohaliWe 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.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.9/ |
| spellingShingle | Sakagaito, Makoto A note on Gersten’s conjecture for étale cohomology over two-dimensional henselian regular local rings Comptes Rendus. Mathématique |
| title | A note on Gersten’s conjecture for étale cohomology over two-dimensional henselian regular local rings |
| title_full | A note on Gersten’s conjecture for étale cohomology over two-dimensional henselian regular local rings |
| title_fullStr | A note on Gersten’s conjecture for étale cohomology over two-dimensional henselian regular local rings |
| title_full_unstemmed | A note on Gersten’s conjecture for étale cohomology over two-dimensional henselian regular local rings |
| title_short | A note on Gersten’s conjecture for étale cohomology over two-dimensional henselian regular local rings |
| title_sort | note on gersten s conjecture for etale cohomology over two dimensional henselian regular local rings |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.9/ |
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