Springer's theorem for tame quadratic forms over Henselian fields

2010/02/05 by Mohamed Abdou Elomary, Jean-Pierre Tignol, Elomary, Mohamed Abdou +1
Mathematics · #11E81 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #K-Theory and Homology (math.KT) #Mathematical Dynamics and Fractals #math.AG #math.KT #msc:11E81

paper · pdf · doi:10.48550/arxiv.1002.1153

arxiv created 2010/02/05 · openalex publication_date 2010/02/05 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A quadratic form over a Henselian-valued field of arbitrary residue characteristic is tame if it becomes hyperbolic over a tamely ramified extension. The Witt group of tame quadratic forms is shown to be canonically isomorphic to the Witt group of graded quadratic forms over the graded ring associated to the filtration defined by the valuation, hence also isomorphic to a direct sum of copies of the Witt group of the residue field indexed by the value group modulo 2.

Related

• The algebra and model theory of tame valued fields
• Elimination of Ramification II: Henselian Rationality
• Generalization of Abhyankar's Lemma to henselian valued fields
• Classes of forms Witt equivalent to a second trace form over fields of characteristic two
• The model theory of separably tame valued fields