Detlev HoffmannAffiliation: University of Nottingham Email: pmzdwh@maths.nottingham.ac.uk Title Of Talk: Differential Forms and Bilinear Forms under Field Extensions Abstract: An important object in the algebraic theory of quadratic forms is the Witt ring of bilinear forms over a field. We are interested in the determination of the kernel of the restriction map from the Witt ring of a field to that of a field extension, the so-called Witt kernel for that field extension. For fields of characteristic not 2, Witt kernels are known only for a few types of field extensions. We determine the Witt kernels in the case of characteristic 2 for all simple algebraic extensions and extensions given by function fields of hypersurfaces. A main tool in the proof concerns the module of differential forms over fields of characteristic two and its behavior under field extensions. We determine more generally the kernel of the restriction map between the module of differential forms over a field of arbitrary positive characteristic and that of an extension field given by a simple algebraic extension or a function field of a hypersurface. An important special case is that of the function field of a diagonal form of degree p in characteristic p.
Last update made Sun May 17 19:56:30 EDT 2009.
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