On the norm residue homomorphism for fields

1996 ◽  
pp. 49-71
Author(s):  
A. S. Merkur′ev
Keyword(s):  
Norm Residue

An Overview of the Proof

2019 ◽  
pp. 3-22
Author(s):  
Christian Haesemeyer ◽  
Charles A. Weibel
Keyword(s):  
Motivic Cohomology ◽  
Norm Residue ◽  
Cohomology Operations ◽  
Definition Of ◽  
Special Case

This chapter provides the main steps in the proof of Theorems A and B regarding the norm residue homomorphism. It also proves several equivalent (but more technical) assertions in order to prove the theorems in question. This chapter also supplements its approach by defining the Beilinson–Lichtenbaum condition. It thus begins with the first reductions, the first of which is a special case of the transfer argument. From there, the chapter presents the proof that the norm residue is an isomorphism. The definition of norm varieties and Rost varieties are also given some attention. The chapter also constructs a simplicial scheme and introduces some features of its cohomology. To conclude, the chapter discusses another fundamental tool—motivic cohomology operations—as well as some historical notes.

The norm residue isomorphism theorem

2009 ◽  
Vol 2 (2) ◽  
pp. 346-372 ◽  
Author(s):  
C. Weibel
Keyword(s):  
Isomorphism Theorem ◽  
Norm Residue

The Norm Residue Theorem in Motivic Cohomology

2019 ◽  
Author(s):  
Christian Haesemeyer ◽  
Charles A. Weibel
Keyword(s):  
Residue Theorem ◽  
Motivic Cohomology ◽  
Norm Residue

scholarly journals An explicit local norm residue symbol

1970 ◽  
Vol 2 (2) ◽  
pp. 143-151
Author(s):  
L Geissinger ◽  
W Graves
Keyword(s):  
Local Norm ◽  
Residue Symbol ◽  
Norm Residue
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