Norm varieties and algebraic cobordism

TL;DR

This paper explores norm varieties and algebraic cobordism, focusing on the bijectivity of the norm residue homomorphism, defining key concepts, and discussing degree formulas and Hilbert's 90 for symbols, building on Voevodsky's theorem.

Contribution

It introduces the concept of norm varieties, discusses their constructions, and formulates Hilbert's 90 for symbols in relation to the norm residue homomorphism.

Findings

Norm varieties are defined and constructed.

Degree formulas are established as tools for analysis.

Hilbert's 90 for symbols is formulated, linking to Voevodsky's theorem.

Abstract

We outline briefly results and examples related with the bijectivity of the norm residue homomorphism. We define norm varieties and describe some constructions. We discuss degree formulas which form a major tool to handle norm varieties. Finally we formulate Hilbert's 90 for symbols which is the hard part of the bijectivity of the norm residue homomorphism, modulo a theorem of Voevodsky.