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arxiv: 1904.02937 · v1 · pith:NGLSAJG6new · submitted 2019-04-05 · 🧮 math.AG · math.KT

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

classification 🧮 math.AG math.KT
keywords nisnevichbloch-oguscohomologyhenselianinfiniteresidueringtheorem
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We show a conditional exactness statement for the Nisnevich Gersten complex associated to an $\mathbb{A}^1$-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 \'etale cohomology over a henselian discrete valuation ring with infinite residue field.

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