Quadratic Descent of Involutions in Degree-2 and Degree-4
(1995) Proceedings of the American Mathematical Society — Vol. 123, n° 7, p. 1963-1969 (1995)
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- Abstract
- If K/F is a quadratic extension, we give necessary and sufficient conditions in terms of the discriminant (resp. the Clifford algebra) for a quadratic form of dimension 2 (resp. 4) over K to be similar to a form over P. We give similar criteria for an orthogonal involution over a central simple algebra A of degree 2 (resp. 4) over K to be such that A = A' X(F) K, where A' is invariant under the involution. This leads us to an example of a quadratic form over K which is not similar to a form over F but such that the corresponding involution comes from an involution defined over F.
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Dherte, H. (1995). Quadratic Descent of Involutions in Degree-2 and Degree-4. Proceedings of the American Mathematical Society, 123(7), 1963-1969. https://hdl.handle.net/2078.5/144893 (Original work published 1995)