Geodesic
Hermitian Forms and Systems of Quadratic Forms
Documenta mathematica, Tome 23 (2018), pp. 747-758
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We associate to every symmetric (antisymmetric) Hermitian form a system of quadratic forms over the base field which determines its isotropy and metabolicity behaviour. It is shown that two even Hermitian forms are isometric if and only if their associated systems are equivalent. As an application, it is also shown that an anisotropic symmetric Hermitian form over a quaternion division algebra in characteristic two remains anisotropic over all odd degree extensions of the ground field.
DOI : 10.4171/dm/632
Classification : 11E04, 11E39
Mots-clés : Hermitian form, system of quadratic forms, division algebra with involution, Springer's theorem 
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     author = {Amir Hossein Nokhodkar},
     title = {Hermitian {Forms} and {Systems} of {Quadratic} {Forms}},
     journal = {Documenta mathematica},
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     doi = {10.4171/dm/632},
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Amir Hossein Nokhodkar. Hermitian Forms and Systems of Quadratic Forms. Documenta mathematica, Tome 23 (2018), pp. 747-758. doi: 10.4171/dm/632

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