by M. Rost (Notes, December 2001, 7 pages)
This is more or less an appendix to Merkurjev's text "Degree Formula" (see below). We show that the invariant \eta_p has the expected description in terms of characteristic numbers. This result is currently needed in the approach to the Bloch-Kato conjecture.
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by A. Merkurjev (Notes, May 2000, 20 pages)
This text contain a short proof of the "degree formula", together with a variety of applications and further considerations. Conjecture 11.2 of this text would imply the "higher degree formula".
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For other texts related with degree formulas see Merkurjev's page Recent Publications and Preprints and
For newer texts on Algebraic Cobordism checkout the home pages of M. Levine and of F. Morel.
Using the degree formula for surfaces, Jean-Louis Colliot-Thélène and David A. Madore constructed Del Pezzo surfaces of degrees 3 and 4 over a field of cohomological dimension 1 having no rational points.