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Splitting patterns and trace forms

  Published:1998-03-01
 Printed: Mar 1998
  • Jurgen Hurrelbrink
  • Ulf Rehmann
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Abstract

The splitting pattern of a quadratic form $q$ over a field $k$ consists of all distinct Witt indices that occur for $q$ over extension fields of $k$. In small dimensions, the complete list of splitting patterns of quadratic forms is known. We show that {\it all\/} splitting patterns of quadratic forms of dimension at most nine can be realized by trace forms.
Keywords: Quadratic forms, Witt indices, generic splitting. Quadratic forms, Witt indices, generic splitting.
MSC Classifications: 11E04 show english descriptions Quadratic forms over general fields 11E04 - Quadratic forms over general fields
 

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