Degree four cohomological invariants for quadratic forms

by Bill Jacob and Markus Rost (20 pages)

Invent. Math. 96 (1989), no. 3, 551-570.

The main result is the existence of the invariant e⁴: I⁴F → H⁴F.

The existence of e⁴ has been proved independently and at about the same time by Marek Szyjewski, see references 1, 2.

Szyjewski calls e⁴ the fifth invariant, probably to emphasize e⁰ (which he considered over schemes, see reference 3).

References:

Szyjewski, Marek (Shyevski, M.). The fifth invariant of quadratic forms. Dokl. Akad. Nauk SSSR 308 (1989), no. 3, 542-545; translation in Soviet Math. Dokl. 40 (1990), no. 2, 355-358. MR 1021111, Zbl 0699.10032.
Szyjewski, Marek (Shyevski, M.). The fifth invariant of quadratic forms. Algebra i Analiz 2 (1990), no. 1, 213-234; translation in Leningrad Math. J. 2 (1991), no. 1, 179-198. MR 1049911, Zbl 0697.10021.
Szyjewski, Marek. An invariant of quadratic forms over schemes. Doc. Math. 1 (1996), No. 19, 449-478. MR 1425300, Zbl 0876.11019.