Durch Normengruppen definierte birationale Invarianten

by Markus Rost (4 pages)

C. R. Acad. Sci. Paris Sér. I Math. 310 (1990), no. 4, 189-192.

MR 1046902, Zbl 711.14004.

This is the only Comptes Rendus Mathématique article in German. Ever!

Let Z be a complete variety over k. We prove the following purity theorem: an element of the function field K of a proper smooth variety X over k, which for any point of X of codimension 1 can be written as a unit times a product of norms from the residue class fields of closed points of ZK, has the same property with respect to any point of X. If X is rational, one may find a global unit with this property.

Full text (may differ slightly from the original article): [tex] [dvi] [dvi.gz] [ps] [ps.gz] [pdf] [pdf.gz]


In typical applications one takes for Z a homogenous projective variety. For instance, if Z is a quadric associated with a Pfister form f, then the group of norms from the residue class fields of closed points of Z is the set of values of f.
The following text uses this for the case f=sum of 2d squares.

Eine Bemerkung zu einem Satz von E. Becker und D. Gondard

von Jean-Louis Colliot-Thélène.

Eberhard Becker zum 60. Geburtstag gewidmet.

Math. Z. 249 3, 2005, 541-543.

MR 2121739.

Full text (December 2003, available here with kind permission of the author): [dvi] [ps] [pdf]


Go to: Publications and Preprints · Markus Rost's Web Page