Linkage of Fields in Characteristic 2

Abstract

Let F be a field with 2 = 0 and ϕ = ⟨⟨a ₁,…,a _n ⟩⟩ an n-fold anisotropic bilinear Pfister form over F with function field F(ϕ). In this paper we compute ker where I _F  ⊂ W(F) is the maximal ideal in the Witt ring W(F) of F. We use this computation to prove an n-linkage property of the subfields F ²(a ₁,…,a _n ).

Keywords:

• Quadratic forms
• Differential forms
• Bilinear forms
• Witt-group
• Function fields
• Linkage of fields

Acknowledgments

The first author was partially supported by Fondecyt 100 0391 and Programa Formas Cuadráticas, U. de Talca. The second author was partially supported by Fondecyt 100 0392 and Programa Formas Cuadráticas, U. de Talca.