Splitting patterns and trace forms

http://dx.doi.org/10.4153/CMB-1998-011-8
Canad. Math. Bull. 41(1998), 71-78

  Published:1998-03-01
 Printed: Mar 1998

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.