A Bloch-Ogus Theorem for henselian local rings in mixed characteristic

2019/04/05 by Johannes Dragsbæk Schmidt, Schmidt, Johannes, Florian Strunk +1 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.1904.02937

openalex publication_date 2019/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show a conditional exactness statement for the Nisnevich Gersten complex associated to an \mathbbA¹-invariant cohomology theory with Nisnevich descent for smooth schemes over a Dedekind ring with only infinite residue fields. As an application we derive a Nisnevich analogue of the Bloch-Ogus theorem for étale cohomology over a henselian discrete valuation ring with infinite residue field.

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• The Bloch-Ogus Theorem over DVR

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• Bloch-Ogus theory for smooth and semi-stable schemes in mixed characteristic
• Variations on the Bloch-Ogus Theorem
• The Bloch-Ogus Theorem over DVR
• Grothendieck local duality and Cohomological Hasse principle
• Henselian schemes in positive characteristic