[Une note sur la conjecture de Gersten pour la cohomologie étale sur des anneaux locaux réguliers henséliens à deux dimensions]
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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Makoto Sakagaito 1

@article{CRMATH_2020__358_1_33_0, 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}, }
TY - JOUR AU - Makoto Sakagaito TI - A note on Gersten’s conjecture for étale cohomology over two-dimensional henselian regular local rings JO - Comptes Rendus. Mathématique PY - 2020 SP - 33 EP - 39 VL - 358 IS - 1 PB - Académie des sciences, Paris DO - 10.5802/crmath.9 LA - en ID - CRMATH_2020__358_1_33_0 ER -
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/
[1] Grothendieck Topologies, Harvard University, 1962 | Zbl
[2] Gersten’s conjecture and the homology of schemes, Ann. Sci. Éc. Norm. Supér., Volume 7 (1974), pp. 181-201 | DOI | MR | Zbl
[3] Quelques problèmes locaux-globaux (2011) (personal notes)
[4] The Bloch–Ogus–Gabber theorem, Algebraic K-theory (Fields Institute Communications), Volume 16, American Mathematical Society, 1997, pp. 31-94 | MR | Zbl
[5] A proof of the absolute purity conjecture (after Gabber), Algebraic geometry 2000, Azumino (Hotaka) (Advanced Studies in Pure Mathematics), Volume 36, Mathematical Society of Japan, 2000, pp. 153-183 | MR | Zbl
[6] Motivic cohomology over Dedekind rings, Math. Z., Volume 248 (2004) no. 4, pp. 773-794 | DOI | Zbl
[7] Local-global principles for Galois cohomology, Comment. Math. Helv., Volume 89 (2014) no. 1, pp. 215-253 | DOI | MR | Zbl
[8] A Cohomological Hasse Principle Over Two-dimensional Local Rings, Int. Math. Res. Not., Volume 2017 (2017) no. 14, pp. 4369-4397 | MR | Zbl
[9] Étale Cohomology, Princeton Mathematical Series, 33, Princeton University Press, 1980 | MR | Zbl
[10] The equicharacteristic case of the Gersten conjecture, Tr. Mat. Inst. Im. V. A. Steklova, Volume 241 (2003) no. 2, pp. 169-178 | MR | Zbl
[11] Arithmetic on two-dimensional local rings, Invent. Math., Volume 85 (1986), pp. 379-414 | DOI | MR | Zbl
[12] On problems about a generalization of the Brauer group (2016) (https://arxiv.org/abs/1511.09232v2)
[13] On a generalized Brauer group in mixed characteristic cases (2019) (https://arxiv.org/abs/1710.11449v2)
[14] On motivic cohomology with
- Bounding cohomology classes over semiglobal fields, Israel Journal of Mathematics, Volume 257 (2023) no. 2, pp. 353-387 | DOI:10.1007/s11856-023-2549-x | Zbl:7893775
- Galois cohomology of function fields of curves over non-Archimedean local fields, Proceedings of the American Mathematical Society, Volume 150 (2022) no. 12, pp. 5179-5191 | DOI:10.1090/proc/16074 | Zbl:1510.12004
- Local-global principles for curves over semi-global fields, Bulletin of the London Mathematical Society, Volume 53 (2021) no. 1, pp. 177-193 | DOI:10.1112/blms.12409 | Zbl:1478.11060
- Local-global principles for curves over semi-global fields, arXiv (2020) | DOI:10.48550/arxiv.2001.05429 | arXiv:2001.05429
- Generalized period-index problem with an application to quadratic forms, arXiv (2019) | DOI:10.48550/arxiv.1910.02473 | arXiv:1910.02473
- On a generalized Brauer group in mixed characteristic cases, arXiv (2017) | DOI:10.48550/arxiv.1710.11449 | arXiv:1710.11449
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