Graded Hermitian forms and Springer's theorem

DOI10.1016/S0019-3577(07)80010-3zbMath1247.11052MaRDI QIDQ2381841

J.-R Tignol, J.-F Renard, Adrian R. Wadsworth

Publication date: 19 September 2007

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

zbMATH Keywords

division ringgraded moduleSpringer's theoremHenselian valuationgraded Hermitian form

Mathematics Subject Classification ID

Algebraic theory of quadratic forms; Witt groups and rings (11E81) Bilinear and Hermitian forms (11E39)

Related Items (13)

Arason's filtration of the Witt group of dyadic valued fields ⋮ Okubo algebras and valuations ⋮ Degree three unramified cohomology of adjoint semisimple groups ⋮ Discriminants of symplectic graded involutions on graded simple algebras. ⋮ \(\text{SK}_1\) of graded division algebras. ⋮ Valuations on algebras with involution. ⋮ Discriminants of orthogonal involutions on central simple algebras with tame gauges. ⋮ Springer's theorem for tame quadratic forms over Henselian fields ⋮ ON GENERALIZED GRADED CROSSED PRODUCTS AND KUMMER SUBFIELDS OF SIMPLE ALGEBRAS ⋮ Outer automorphisms of classical algebraic groups ⋮ Value functions and associated graded rings for semisimple algebras ⋮ Value functions and Dubrovin valuation rings on simple algebras ⋮ Strongly Anisotropic Involutions on Central Simple Algebras

Cites Work

• Division algebras over Henselian fields.
• A Springer theorem for Hermitian forms.
• Quadratic forms over dyadic valued fields. I: The graded Witt ring
• The Henselization of a valued division algebra
• Über die Grade quadratischer Formen
• Correspondences between valued division algebras and graded division algebras
• The space of p-adic norms
• Klassifikation hermitescher Formen über lokalen Körpern
• HENSELIAN VALUATIONS OF DIVISION RINGS AND THE GROUPSK₁
• Schémas en groupes et immeubles des groupes classiques sur un corps local
• Extending Valuations to Finite Dimensional Division Algebras
• The witt ring of a graded field
• Schémas en groupes et immeubles des groupes classiques sur un corps local. II : groupes unitaires
• REDUCED UNITARYK-THEORY AND DIVISION RINGS OVER DISCRETELY VALUED HENSEL FIELDS
• Algebraic extensions of graded and valued fields
• Le gradué d’une algèbre à division valuée
• Versions of Springer's Theorem for Quadratic Forms in Characteristic 2
• Finite-Dimensional Division Algebras over Fields
• Valued Fields
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