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.
Full text (version of December 13, 2001): [pdf]
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".
Full text: [pdf]
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.