Nisnevich Topology

In algebraic geometry, the Nisnevich topology, sometimes called the completely decomposed topology, is a Grothendieck topology on the category of schemes which has been used in algebraic K-theory, A¹ homotopy theory, and the theory of motives. It was originally introduced by Yevsey Nisnevich, who was motivated by the theory of adeles.

Read more about Nisnevich TopologyDefinition, Local Rings in The Nisnevich Topology, Applications

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Nisnevich Topology - Applications
... Nisnevich introduced his topology to provide a cohomological interpretation of the class set of an affine group scheme, which was originally defined in adelic terms ... scheme over an integral regular Noetherian base scheme is locally trivial in the Zariski topology ... One of the key properties of the Nisnevich topology is the existence of a descent spectral sequence ...