Norm varieties and algebraic cobordism

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.

References in corpus (1)

• Algebraic cobordism

Cited by in corpus (11)

• On pro-$p$ groups with quadratic cohomology
• Profinite groups with a cyclotomic $p$-orientation
• Mild pro-p groups and the Koszulity conjectures
• Right-angled Artin pro-$p$ groups
• Involutions of varieties and Rost's degree formula
• One relator maximal pro-p Galois groups and the Koszulity conjectures
• Cohomology operations and algebraic geometry
• Frattini-injectivity and Maximal pro-$p$ Galois groups
• Notes on the Milnor conjectures
• Geometric criteria for ${\mathbb{A}}^1$-connectedness and applications to norm varieties
• Bertini theorems and Lefschetz pencils over discrete valuation rings, with applications to higher class field theory