Vishik equivalence and similarity of quasilinearp-forms and totally singular quadratic forms
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Bibliographic record
Abstract
For quadratic forms over fields of characteristic different from two, there is a so-called Vishik criterion, giving a purely algebraic characterization of when two quadratic forms are motivically equivalent.In analogy to that, we define Vishik equivalence on quasilinear p-forms.We study the question whether Vishik equivalent p-forms must be similar.We prove that this is not true for quasilinear p-forms in general, but we find some families of totally singular quadratic forms (i.e., of quasilinear 2-forms) for which the question has a positive answer.Question A. Are quadratic forms satisfying Vishik's criterion (1-1) necessarily similar?Izhboldin [1998; 2000] proved that the answer to Question A is positive for odddimensional quadratic forms, but negative for even-dimensional forms of dimension greater or equal to 8 (except possibly for the dimension 12).Hoffmann [2015] proves that, under some conditions on the base field, Question A has positive answer for even-dimensional quadratic forms as well.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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