Garibaldi S. Cohomological invariants: exceptional groups and spin groups / with an appendix by Hoffmann D.W. - Providence: American Mathematical Society, 2009. - xii, 81 p.: ill. - (Memoirs of the American Mathematical Society; Vol.200, N 937). - Bibliogr.: p.77-80. - Ind.: p.81. - ISBN 978-0-8218- 4404-5; ISSN 0065-9266  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Contents

List of Tables ................................................. ix Preface ........................................................ xi Part I. Invariants, especially modulo an odd prime .............. 1 1. Definitions and notations .................................... 2 2. Invariants of μn ............................................. 5 3. Quasi-Galois extensions and invariants of /p .............. 7 4. An example: the mod p Bockstein map ......................... 10 5. Restricting invariants ...................................... 12 6. Mod p invariants of PGLP .................................... 14 7. Extending invariants ........................................ 17 8. Mod 3 invariants of Albert algebras ......................... 19 Part II. Surjectivities and invariants of Е6, E7, and Е8 ........ 23 9. Surjectivities: internal Chevalley modules .................. 24 10. New invariants from homogeneous forms ...................... 29 11. Mod 3 invariants of simply connected E6 .................... 31 12. Surjectivities: the highest root ........................... 33 13. Mod 3 invariants of Е7 ..................................... 38 14. Construction of groups of type E8 .......................... 39 15. Mod 5 invariants of E8 ..................................... 44 Part III. Spin groups .......................................... 47 16. Introduction to Part III ................................... 48 17. Surjectivities: Spinn for 7 ≤ n ≤ 12 ....................... 48 18. Invariants of Spinn for 7 ≤ n ≤ 10 ......................... 53 19. Divided squares in the Grothendieck-Witt ring .............. 56 20. Invariants of Spinn and Spin12 ............................. 58 21. Surjectivities: Spin14 ..................................... 61 22. Invariants of Spin14 ....................................... 65 23. Partial summary of results ................................. 66 Appendices ..................................................... 69 A. Examples of anisotropic groups of type E7 ................... 70 B. A generalization of the Common Slot Theorem ................. 73 By Detlev W. Hoffmann Bibliography ................................................... 77 Index .......................................................... 81