Copy of my home page at IAS in the Academic Year 2004-2005. Original URL of this page: http://www.math.ias.edu/~rost

Welcome to the home page of Markus Rost at IAS (2004-2005).

My office is F-203 (in Fuld Hall), phone: 609-734-8294, email:

Here is a link to my home page in Bielefeld.

Seminar on Norm Varieties (A. Suslin and M. Rost)

For the schedule see Math Seminars at IAS. The usual time/room is Wednesdays, 2:00pm - 3:00pm/S-101.

Andrei Suslin's lectures (October-December 2004)

Notes by Seva Joukhovitski.

Update 2006: The text has appeared as [Suslin and Joukhovitski, Norm varieties, J. Pure Appl. Algebra 206 1-2, 2006, 245-276], MR 2220090

Update 2005: See K-theory Preprint Archives, Preprint 742

"This is a preliminary version that we feel to be sufficiently complete and typo - free. An updated version that will contain a proof of the Theorem 2.4 will hopefully be available sometime soon."

• Norm_Varieties.dvi
• Norm_Varieties.pdf

Markus Rost's lectures (January-March 2005)

Here are preliminary notes by Christian Haesemeyer:

• http://www.math.ias.edu/~chh (there might be several versions, the dates are indicated in the file names).
• chain02-07-2005.dvi · chain02-07-2005.ps · chain02-07-2005.ps.gz - local copy

Related texts

This list is just meant for reference in the seminar and is not complete at all. For more see the Chain Lemma page. A lot of related bibliography can be found on the page Lectures on Norm Varieties at IAS 1999-2000.

On "Theorem DN"

• My short text: theorem-DN.pdf
• Links to K-theory server for Levine/Morel: M. Levine and F. Morel, Algebraic cobordism I, preprint, 2002. In this text M. Levine and F. Morel give a proof of all the necessary "higher degree formulas". Checkout the home pages of M. Levine and of F. Morel. Morel's Web pages seem to contain a newer version.
• Links to AMS Math Reviews for the other texts: Mitchel's article, The book of Conner and Floyd and Floyd's article. I have a copy of Floyd's article.
• Mitchel's article is available on-line: A Proof of the Conner-Floyd Conjecture, Stephen A. Mitchell, American Journal of Mathematics, Vol. 106, No. 4. (Aug., 1984), pp. 889-891. Stable URL: http://links.jstor.org/sici?sici=0002-9327%28198408%29106%3A4%3C889%3AAPOTCC%3E2.0.CO%3B2-E

On the Chain Lemma for central simple algebras of prime degree

• For p=3 the morphism h_4 has a rational section. Here is the proof: The chain lemma for Kummer elements of degree 3
• The computation of deg(h_3)=2 (for p=3) can be found here (Ch. V, §13, pp. 117-123): On Twisted Cyclic Algebras and the Chain Equivalence of Kummer Elements. Maybe I will write a few separate pages containing that computation (here is an incomplete first version).

Chain lemma for splitting fields of symbols

by Markus Rost (Preliminary text for a paper in preparation, August 1998, 18 pages)

This text contains the construction of various parameter spaces for chains together with the computation of the degrees of the highest power of c_1 of certain line bundles.

It contains all details concerning multiplicativity.

The computations for the rings R(a,b) can be found on pages 10-12.

Full text: [dvi] [dvi.gz] [ps] [ps.gz]

Construction of splitting varieties

by Markus Rost (Preprint, April 1998, 30 pages)

This text contains some explanations of our approach and details on the construction of various splitting varieties for symbols. A good part of it had been simplified later, but it is still the only place where we discuss the norm principle in detail.

The computations for the rings R(a,b) can be found on pages 14-16 (but better use the other text for this).

Full text: [dvi] [dvi.gz] [ps] [ps.gz]

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