Differential forms and bilinear forms under field extensions

JOURNAL OF ALGEBRA

卷:441

Article

Dolphin, Andrew¹  Hoffmann, Detlev W.² 

[1] Univ Antwerp, Dept Wiskunde & Informat, B-2020 Antwerp, Belgium

[2] Tech Univ Dortmund, Fak Math, D-44221 Dortmund, Germany

关键词: Bilinear form;    Witt ring;    Witt kernel;    Differential form;    Simple extension;    Separable extension;    Inseparable extension;    Function field;    Hypersurface;    Milnor K-theory;   

DOI  :  10.1016/j.jalgebra.2015.05.034

来源: Elsevier

【 摘 要 】

Let F be a field of characteristic p > 0. Let Omega(n)(F) be the F-vector space of n-differentials of F over F-p. Let K = F(g) be the function field of an irreducible polynomial g in in m >= 1 variables over F. We derive an explicit description of the kernel of the restriction map Omega(n)(F) -> Omega(n)(K). As an application in the case p = 2, we determine the kernel of the restriction map when passing from the Witt ring (rasp. graded Witt ring) of symmetric bilinear forms over F to that over such a function field extension K. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free