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Please use this identifier to cite or link to this item: http://dspace.utalca.cl/handle/1950/3835

Title: The behavior of quadratic and differential forms under function field extensions in characteristic two
Authors: Baeza, R.
Aravire, R.
Keywords: Quadratic forms,Differential forms,Bilinear forms,Witt-groups,Function fields,Generic splitting fields of quadratic forms,Degree of quadraticforms
Issue Date: 2003
Publisher: Elsevier Science (USA)
Citation: Journal of Algebra 259 (2):361–414
Abstract: Let F be a field of characteristic 2. Let ΩnF be the F-space of absolute differential forms over F. There is a homomorphism :ΩnF→ΩnF/dΩn−1F given by (x dx1/x1dxn/xn)=(x2−x) dx1/x1dxn/xn mod dΩFn−1. Let Hn+1(F)=Coker(). We study the behavior of Hn+1(F) under the function field F(φ)/F, where φ=b1,…,bn is an n-fold Pfister form and F(φ) is the function field of the quadric φ=0 over F. We show that . Using Kato's isomorphism of Hn+1(F) with the quotient InWq(F)/In+1Wq(F), where Wq(F) is the Witt group of quadratic forms over F and IW(F) is the maximal ideal of even-dimensional bilinear forms over F, we deduce from the above result the analogue in characteristic 2 of Knebusch's degree conjecture, i.e. InWq(F) is the set of all classes
Description: Baeza R. Instituto de Matemática y Física,Universidad de Talca,Casilla 747,Talca,Chile.
URI: http://dspace.utalca.cl/handle/1950/3835
ISSN: 0021-8693
Appears in Collections:Artículos en publicaciones ISI - Universidad de Talca

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