Abstract
The goal of this paper is to present proofs of two results of Markus Rost, the Chain Lemma 1 and the Norm Principle 3. These are the steps needed to complete the published verification of the Bloch– Kato conjecture, that the norm residue maps are isomorphisms for every prime p, every n and every field k containing 1/ p.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
C. Weibel, Axioms for the Norm Residue Isomorphism, pp. 427–436 in K-theory and Non-commutative Geometry, European Math. Soc., 2008. Also available at http://www.math.uiuc.edu/K-theory/0809/.
C. Weibel, Patching the Norm Residue Isomorphism Theorem, Preprint, 2007. Available at http://www.math.uiuc. edu/K-theory/0844/.
A. Suslin and S. Joukhovitski, Norm Varieties, J. Pure Appl. Algebra 206 (2006), 245–276.
V. Voevodsky, On Motivic Cohomology with \(\mathbb{Z}\)/l coefficients, Preprint, 2003. Available at http://www.math.uiuc. edu/K-theory/0639/.
M. Rost, Chow groups with coefficients, Doc. Math. J. DMV 1 (1996), 319–393.
M. Rost, Construction of Splitting Varieties, Preprint, 1998. Available at http://www.math.uni-bielefeld.de/r̃ost/chain-lemma.html
M. Rost, Chain lemma for splitting fields of symbols, Preprint, 1998. Available at http://www.math. uni-bielefeld.de/r̃ost/chain-lemma.html
M. Rost, Notes on Lectures given at IAS, 1999–2000 and Spring Term 2005.
J. Milnor and J. Stasheff, Characteristic Classes, Princeton University Press, 1974.
R. Stong, Notes on Cobordism Theory, Princeton University Press, 1968.
J. F. Adams, Stable homotopy and generalised homology, University of Chicago Press, 1974.
A. Merkurjev and A. Suslin, K-cohomology of Severi-Brauer varieties, Izv. Akad. Nauk SSSR Ser. Mat. 46 (1982), 1011–1046 (Russian). English translation Math. USSR Izvestiya 21 (1983), 307–340.
A. Weil, Adeles and Algebraic Groups, Birkhäuser, 1982. Based on lectures given 1959–1960.
M. Rost, The chain lemma for Kummer elements of degree 3. C. R. Acad. Sci. Paris Sér. I Math., 328(3) (1999), 185–190.
M. Levine and F. Morel, Algebraic Cobordism, Springer Monographs in Mathematics, 2007.
T. tom Dieck, Actions of finite abelian p-groups without stationary points, Topology 9 (1970), 359–366.
P. Conner and E. Floyd, Periodic maps which preserve a complex structure, Bull. Am. Math. Soc. 70 (1964), 574–579.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Haesemeyer, C., Weibel, C. (2009). Norm Varieties and the Chain Lemma (After Markus Rost). In: Baas, N., Friedlander, E., Jahren, B., Østvær, P. (eds) Algebraic Topology. Abel Symposia, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01200-6_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-01200-6_6
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-01199-3
Online ISBN: 978-3-642-01200-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)