# 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, but no
introduction and is perhaps hard to digest.

Full text: [dvi]
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The construction of splitting varieties via parameter spaces of
chains turned out to be useful for further questions related to the
Bloch-Kato conjecture, see

See also

- A. Suslin and S. Joukhovitski, Norm varieties, J. Pure
Appl. Algebra 206 1-2, 2006, 245-276,
MR
2220090

Here are some older variants:

### Chain lemma for splitting fields of symbols

by Markus Rost (Introduction to a paper in preparation, September
1997, 12 pages)

This is just the introduction of the first version of a preprint
with details on the chain lemma. It is in parts meanwhile obsolete.
We still offer it here, since the other texts do not contain any
introduction at all.

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### 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.

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