Pairs of quadratic forms over a quadratic field extension |
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Authors: | A.S. Sivatski |
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Affiliation: | Departamento de Matemática, Universidade Federal do Rio Grande do Norte, Natal, Brazil |
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Abstract: | Let F be a field of characteristic distinct from 2, a quadratic field extension. Let further f and g be quadratic forms over L considered as polynomials in n variables, , their matrices. We say that the pair is a k-pair if there exist such that all the entries of the upper-left corner of the matrices and are in F. We give certain criteria to determine whether a given pair is a k-pair. We consider the transfer determined by the -linear map with , , and prove that if , then is a -pair. If, additionally, the form does not have a totally isotropic subspace of dimension over , we show that is a -pair. In particular, if the form is anisotropic, and , then is a k-pair. |
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Keywords: | 11E04 11E81 |
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