Andrew Dolphin and Detlev W. Hoffmann: Differential forms and bilinear forms under field extensions and

Submission: 2011, Apr 1

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 m> 0 variables over F. We derive an explicit description of the kernel of the restriction map from Omega^n(F) to 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 (resp. graded Witt ring) of symmetric bilinear forms over F to that over such a function field extension K.

2010 Mathematics Subject Classification: Primary 11E81; Secondary 11E39, 12F05; 12F10; 12F15; 12F20; 12H05; 19D45

Keywords and Phrases: Bilinear form; Witt ring; Witt kernel; differential form; Kåhler differential; Milnor K-theory; function field; simple extension; separable extension; inseparable extension.

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