Witt kernels of quadratic forms for multiquadratic extensions in characteristic 2

2014/03/07 by Detlev W. Hoffmann, Hoffmann, Detlev W.
Mathematics · #11E04 (Primary) 11E81 #12F15 (Secondary) #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA) #math.AC #math.RA #msc:11E04 #msc:11E81 #msc:12F15

paper · pdf · doi:10.48550/arxiv.1403.1802

9 pages

arxiv created 2014/03/07 · arxiv updated 2014/03/10

Abstract

Let F be a field of characteristic 2 and let K/F be a purely inseparable extension of exponent 1. We show that the extension is excellent for quadratic forms. Using the excellence we recover and extend results by Aravire and Laghribi who computed generators for the kernel W_q(K/F) of the natural restriction map W_q(F)→ W_q(K) between the Witt groups of quadratic forms of F and K, respectively, where K/F is a finite multiquadratic extension of separability degree at most 2.

Related

• Witt kernels and Brauer kernels for quartic extensions in characteristic two
• The behavior of differential, quadratic and bilinear forms under purely inseparable field extensions
• The Witt groups of extended quadratic forms over Z
• Some Galois extensions of quadratic extensions associated with Witt rings
• Classes of forms Witt equivalent to a second trace form over fields of characteristic two