English

Norm Varieties and the Chain Lemma (after Markus Rost)

K-Theory and Homology 2008-06-23 v1 Algebraic Geometry

Abstract

The goal of this paper is to present proofs of two results of Markus Rost: the Chain Lemma and the Norm Principle. These are the final steps needed to complete the publishable verification of the Bloch-Kato conjecture, that the norm residue maps are isomorphisms between Milnor K-theory KnM(k)/pK_n^M(k)/p and etale cohomology Hn(k,μpn)H^n(k,\mu_p^n) for every prime p, every n and every field k containing 1/p. Our proofs of these two results are based on Rost's 1998 preprints, his web site and Rost's lectures at the Institute for Advanced Study in 1999-2000 and 2005.

Cite

@article{arxiv.0806.3421,
  title  = {Norm Varieties and the Chain Lemma (after Markus Rost)},
  author = {Christian Haesemeyer and Charles A. Weibel},
  journal= {arXiv preprint arXiv:0806.3421},
  year   = {2008}
}
R2 v1 2026-06-21T10:52:54.545Z