The Bloch-Ogus Theorem over DVR

2025/06/07 by Gaidai-Turlov, Ivan
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.06892

Abstract

We prove the Bloch-Ogus Theorem for regular local rings geometrically regular over a discrete valuation ring. In particular, we prove the Bloch-Ogus Theorem for regular local rings of mixed characteristic that are essentially smooth over a discrete valuation ring.

Citations

• Constant case of the Grothendieck-Serre conjecture in mixed characteristic
• Moving lemmas in mixed characteristic and applications
• Bloch-Ogus theory for smooth and semi-stable schemes in mixed characteristic
• A Bloch-Ogus Theorem for henselian local rings in mixed characteristic

Related

• A Bloch-Ogus Theorem for henselian local rings in mixed characteristic
• Bloch-Ogus theory for smooth and semi-stable schemes in mixed characteristic
• A special form of Zariski's Uniformization Theorem in positive characteristic
• Local Gersten's conjecture for regular system of parameters
• Mixed characteristic homological theorems in low degrees