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Round quadratic forms
under algebraic extensions
Burkhard Alpers |
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Vol. 147 (1991), No. 2, 213–229
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Abstract |
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Pfister forms over fields are those anisotropic forms that remain round under any field extension. Here, round means that for any represented element x≠0 the isometry xφ≅φ holds where φ is the form under consideration. We investigate whether a similar characterization can be given for the round forms themselves. We obtain several “going-up” and “going-down” theorems. Some counter-examples are given which show that a general theorem holds neither in the going-up nor in the going-down situation. |
Mathematical Subject Classification 2000
Primary: 11E81
Secondary: 12D15
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Milestones
Received: 18 January 1989
Revised: 6 July 1989
Published: 1 February 1991
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Authors |
| Burkhard Alpers | |
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