A Nisnevich local Bloch-Ogus theorem over a general base

A Nisnevich local Bloch-Ogus theorem over a general base

We prove the exactness of the Nisnevich Gersten complex over a Noetherian irreducible base of finite type under some conditions. We also obtain, as a consequence, a Nisnevich analogue of the Bloch-Ogus theorem for étale cohomology in this setting.

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Veröffentlicht in:Journal of pure and applied algebra 2022-06, Vol.226 (6), p.106978, Article 106978
Hauptverfasser: Deshmukh, Neeraj, Kulkarni, Girish, Yadav, Suraj
Format: Artikel
Sprache:eng
Schlagworte:
Gabber's purity theorem
Gersten resolution
Étale cohomology
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Zusammenfassung:We prove the exactness of the Nisnevich Gersten complex over a Noetherian irreducible base of finite type under some conditions. We also obtain, as a consequence, a Nisnevich analogue of the Bloch-Ogus theorem for étale cohomology in this setting.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2021.106978