Fix a symbol a̲ in the mod-ℓ Milnor K-theory of a field k, and a norm variety X for a̲. We show that the ideal generated by a̲ is the kernel of the K-theory map induced by k⊂ k(X) and give generators for the annihilator of the ideal. When ℓ= 2 , this was done by Orlov, Vishik and Voevodsky.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Geometry and Topology
- Milnor K-theory
- Norm variety