Tsukamoto’s Theorem in Characteristic two

Santos, Clotilzio Moreira dos

doi:10.5269/bspm.v32i1.19841

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U-invariants Of Quaternion Algebras1

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“…We call a field F of characteristic 2 a local field if F ≃ F 2 n ((t)). That is, a Laurent series in one variable over F 2 n , the field with 2 n elements for some n ∈ N. In [25] it was shown that u + (Q) = 2 in the case where F is a local field. Corollary 6.8 gives a different proof of this fact, as F = F 2 (t) and hence [F : F 2 ] = 2.…”

Section: U-invariants Of Quaternion Algebrasmentioning

confidence: 99%

Generalised quadratic forms and the u-invariant

Dolphin

2018

Journal of Algebra

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Abstract. The u-invariant of a field is the supremum of the dimensions of anisotropic quadratic forms over the field. We define corresponding u-invariants for hermitian and generalised quadratic forms over a division algebra with involution in characteristic 2 and investigate the relationships between them. We investigate these invariants in particular in the case of a quaternion algebra and futher when this quaternion algebra is the unique quaternion division algebra over a field.

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Section: U-invariants Of Quaternion Algebrasmentioning

confidence: 99%