Formes antihermitiennes devenant hyperboliques sur un corps de déploiement

Dejaiffe, I
(2001) Comptes rendus de l’Académie des sciences - Series I - Mathematics — Vol. 332, n° 2, p. 105-108 (2001)

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  • Dejaiffe, I
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Abstract
Let H = (a, b)(F) be a division quaternion algebra over a field F of characteristic not 2. Denote by tau the canonical involution on H and by K a splitting field of H. If h is a skew-hermitian form over (H,tau) then, by extension of scalars to K and by Morita equivalence, we obtain a quadratic form h(K) over K. This gives a map of Witt groups rho :W-1(H,r) --> W(K) induced by rho (h) = h(K). When K is a generic splitting field of H we prove in this note that the map rho is injective. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.
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Dejaiffe, I. (2001). Formes antihermitiennes devenant hyperboliques sur un corps de déploiement. Comptes rendus de l’Académie des sciences - Series I - Mathematics, 332(2), 105-108. https://doi.org/10.1016/S0764-4442(00)01764-X (Original work published 2001)