Contents
Introduction 5
Chapter I . Th e notio n o f "invariant " 7
1. Definition s 7
2. Example s o f functors A 7
3. Torso r interpretatio n o f the abov e example s 9
4. Example s o f functors H 10
5. Versa l object s 1
Chapter II . Cohomologica l preliminaries : th e loca l cas e 15
6. A n exac t sequenc e 15
7. Galoi s cohomolog y o f local fields 17
8. Functorialit y o f the restrictio n an d corestrictio n 19
Chapter III . Cohomologica l preliminaries : th e functio n field cas e 2 3
9. Galoi s cohomolog y o f k(t) 2 3
10. Galoi s cohomolog y o f k{t\, ..., t n) 2 7
Chapter IV . Specializatio n propertie s o f cohomological invariant s 2 9
11. Compatibilit y wit h goo d reductio n 2 9
12. Specializatio n propertie s 3 1
Chapter V . Restrictio n an d corestrictio n o f invariants 3 3
13. Restrictio n o f invariants 3 3
14. Corestrictio n o f invariants 3 4
15. Stabilit y 3 6
Chapter VI . Cohomologica l invariant s o f O
n
, SO
n
, .. . 3 9
16. Cohomologica l invariant s o f (2,... , 2) group s 3 9
17. Cohomologica l invariant s o f Quad
n
4 1
18. Cohomologica l invariant s o f Pfister
n
an d Oc t 4 3
19. Cohomologica l invariant s o f Quad
n s
( n odd ) 4 4
20. Cohomologica l invariant s o f Quad
n s
(n even ) 4 6
21. Cohomologica l invariant s o f hermitian form s 4 8
22. Cohomologica l invariant s o f Albert algebra s 4 9
23. Cohomologica l invariant s mo d 2 m 5 2
Chapter VII . Cohomologica l invariant s o f etale algebra s 5 5
24. Propertie s o f cohomological invariant s o f Et
n
5 5
25. Cohomologica l invariant s o f Et
n
5 7
26. Application s t o negligibl e cohomolog y 6 1
3
http://dx.doi.org/10.1090/ulect/028/01
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